Also known as "Godhood".

John Wycliffe was the first who added this word to the Bible in 14th century to explain the Trinity.

the nature of God especially as existing in three persons -- Merriam-Webster Dictionary

The word Trinity cannot be found in the Bible, but the truth of it can. While there's only one God, the Godhead consists of three distinct persons - the Father, Son, and Holy Spirit. All are equally omniscient, omnipotent, omnipresent, eternal, and unchanging, but each has unique functions. -- Christianity.com

In theological studies, the term Godhead is used to refer to the concept of the Triune God, or one God in three Persons that include God the Father, God the Son, and God the Holy Spirit. -- Got Questions Ministries

Various scholars attempted to explain the Godhead.

However, Jesus teaching a different kind of "Godhead" theology in the Gospel of John 13-17.

Translations

There are only 3 instances where the English word "Godhead" are found the King James Version (KJV) of the bible and some other modern English bible translations does not even contain that word at all.

Translations of "Godhead":

Because there are so few verses about "Godhead", many theologians came up with different interpretations about what God and/or Jesus could be.

The word "Godhead" is translated from different Greek words:

Theios

Forasmuch then as we are the offspring of God, we ought not to think that the Godhead theios is like unto gold, or silver, or stone, graven by art and man's device. -- Acts 17:29 (KJV)

According to Strong's Concordance:

However, this word is missing in the New King James Version (NKJV) from the same scripture:

Therefore, since we are the offspring of God, we ought not to think that the Divine Nature is like gold or silver or stone, something shaped by art and man’s devising. -- Acts 17:29 (NKJV)

Theiotēs

For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead theiotēs, so that they are without excuse -- Romans 1:20 (NKJV)

Theotés

For in Him dwells all the fullness of the Godhead theotés bodily. -- Colossians 2:9 (NKJV)

The "unified" God

Unitarians often argue that there is only one God, however Trinitarians argue that "God is one" actually means "God is unified" which is supposed to mean "God is a unification of 3 united members".

"echad" has a wider range of usage that includes composite unities as well. -- Jason Dulle

For example, "echad" means unified in:

Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one [echad] flesh. -- Genesis 2:24 (ESV)

Therefore, Trinitarians would apply the same "unified" meaning to "echad" in:

"And the Lord will be king over all the earth; in that day the Lord will be the only one [echad], and His name the only one [echad]." -- Zechariah 14:9

and

"Hear, O Israel! Yahweh is our God, Yahweh is one [echad]!" -- Deuteronomy 6:4

However, when Jesus quoted Deuteronomy 6:4, the Greek translation uses the word "heis" which means single or numerical one:

And Jesus answered him, The first of all the commandments is, Hear, O Israel; The Lord our God is one [heis] Lord. -- Mark 12:29 (KJV)

Another example of "heis" is:

For there is one [heis] God, and there is one [heis] mediator between God and men, the man Christ Jesus... -- 1 Timothy 2:5 (NKJV)

This verse also use "heis" for God's "oneness" as well as to refer to Jesus our mediator. The same word cannot have two different meanings in the same sentence. If "heis" means "united" then the "mediator" must also be united of more members which mean we have more than one mediator between God and men, which contradict Jesus (John 14:6).

Another example where "echad" means "one":

Have we not all one [echad] Father? Has not one [echad] God created us? -- Malachi 2:10 (KJV)

In the same sentence "echad" is used for both the Father and God, therefore "/echad" must have the same meaning for both. If "echad" meant unified one, then it would mean that the Father also unified of smaller gods, or we should accept that there is really only one God, namely the Father Who created us.

There are also examples that demonstrate that God is really the single God or only one God:

The Greek word "hen" usually mean "one", but some scholars argue that because Jesus and his Father is "hen" it means they are unified:

My sheep hear my voice, and I know them, and they follow me: And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand. My Father, which gave them me, is greater than all; and no man is able to pluck them out of my Father's hand. I and my Father are "hen". -- John 10:27-30 (KJV)

In this context, it makes more sense that nobody can pluck Jesus' disciples "out of his hand", nor "out of his Father's hand" because they are the "only" ones who would be with them ("give them eternal life").

And the scribe said unto him, Well, Master, thou hast said the truth: for there is one [hen] God ; and there is none other but He. -- Mark 12:32 (KJV)

In the New Testament Greek, Paul wrote (after Jesus' crucifixion, after Jesus' ascended, after Jesus was exulted, after he personally meet Christ Jesus):

Now unto the King eternal, immortal, invisible, the only [monos] wise God, be honour and glory for ever and ever. -- 1 Timothy 1:17 (KJV)

and

For there is one God, and there is one mediator between God and men, the man Christ Jesus... -- 1 Timothy 2:5 (NKJV)

Jason Dulle argue:

Echad is used nearly 1000 times in the OT, and almost always refers to a single numerical entity. There are times when it is used of a composite entity (Genesis 2:24). It functions just like the English word “one,” which can be used of single or composite entities, although it most often refers to a single, solitary thing. Only the context can determine how echad is being used. Given the rarity with which echad is used to refer to a composite entity, we should understand echad as referring to a single entity unless there are good contextual clues that warrant the uncommon meaning. So given the lexical data alone, the best one could argue is that the semantical domain of echad allows for a Trinitarian understanding of “one,” but by no means does it prove it, and by no means does it rule out the understanding of God’s oneness as an absolute unity.

The question, then, comes down to context. Is there anything in the context of Deuteronomy 6:4 – or any other passage of Scripture in which God is described as being echad – that requires the meaning of composite unity? Meaning is not determined by a words semantical domain, but by the context. To demonstrate that echad means a composite entity with reference to God, the context must make it clear that this is the meaning intended by the author. For example, in Genesis 2:24 man and woman are described as being “echad flesh.” It is physically impossible for man and woman to be considered a single physical entity, so the author must mean “one” in the sense of a composite entity. Are there similar contextual clues that make it clear that echad is being used in this way in Deuteronomy 6:4? No. Indeed, given how God’s oneness is described in passages like Isaiah 42:8 and 44:24, we have very good grounds for understanding the nature of God’s oneness to be that of a numerically single entity.

...

Yachid is also used to describe the emotion of feeling alone (Psalm 25:16) or being alone (Psalm 68:6), and even the uniqueness or precious nature of something (Psalm 22:21; 35:17). The word is never used as a general term for “one.” Its meaning is more akin to “unique” or “only.” Indeed, Isaac is described as Abraham’s yachid even though Isaac was not his only son (Ishmael was born earlier). While God could have been described using yachid, it would not necessarily tell us how many gods there are, but rather what kind of God YHWH is: a unique God. If we want to know how many gods there are, the most appropriate word is echad.

The "plural" God

In the Hebrew language, the word "elohim" usually means multiple gods. The Trinitarians claim that this refers to the multiple personalities God have or the unity of multiple persons in the godhead.

However, in the Bible, the word "elohim" could also technically be considered a singular God for example both Genesis and Exodus (or Shemoth as it is called in The Scriptures) was written by the same author, Moses, who also wrote:

So יהוה said to Mosheh, “See, I have made you an elohim to Pharaoh, and Aharon your brother is your prophet. -- Shemoth/Exodus 7:1 (TS2009)

“He who slaughters to an elohim, except to יהוה only, is put under the ban. -- Shemoth/Exodus 22:20 (TS2009)

This style of writing was not limited to Moses only. In the book of Judges we read that both Baal and Chemosh were also considered "elohim", yet none of them were composite gods.

But Joash said to all who stood against him, “Will you contend for Baal? Or will you save him? Whoever contends for him shall be put to death by morning. If he is a god (elohim, let him contend for himself, because his altar has been broken down.” -- Judges 6:31 (ESV)

Will you not possess what Chemosh your god (elohim gives you to possess? And all that the LORD (YHVH)) our God (elohim has dispossessed before us, we will possess. -- Judges 11:24 (ESV)

The same verse uses the same word "elohim" to refer to either Chemosh or YHVH. Likewise, in 1 Samuel 5:7 the same verse uses the same word "elohim" to refer to either Dagon or YHVH.

And when the men of Ashdod saw how things were, they said, “The ark of the God (elohim) of Israel must not remain with us, for his hand is hard against us and against Dagon our god (elohim).” -- 1 Samuel 5:7 (ESV))

Yet, no one claimed that Dagon was a composite or "uniplural" god or that the people who worshipped Dagon thought that he was one.

However, Mike Leake from Bible Study Tools explains:

The term "Elohim" means “supreme one” or “mighty one.” It is not only used of the one true God but is also used on occasion to refer to human rulers, judges, and even angels. If you saw one exhibiting supreme rule and expressed mighty power, the word you would use would be Elohim.

In the Ancient Near East, it was common to refer to the deity in the compound plural, and when speaking of an owner or master, it was often the rule to speak of him in such terms.

To give you just a few examples,

• Abraham’s servant speaks of his master in the plural in Genesis 24 (ʾadonim, literally, “lords”),
• Joseph speaks of his master Potiphar in the plural in Genesis 39, and
• David the king is spoken of as “lords” in 1 Kings 1:11.
• In Exodus 21, to translate literally and incorrectly, the law speaks of a slave and his masters (ʾadonim, referring to just one master),
• in Isaiah 19:4, the prophet tells Israel that God will hand them over to a cruel lord (Hebrew, ʾadonim qasheh, a plural noun with a singular adjective), and
• Isaiah 1:3 tells us that a donkey knows the feeding crib of its masters (baʾalim, referring to just one person; cf. the first half of the verse in which reference is made to an ox’s owner—in the singular).

These examples, which are really very common, show clearly that compound plurals were often used to speak of leaders, owners, masters, or kings. How much more then could similar expressions be used to speak of the Lord, the Master, the King, and the God."

-- Answering Jewish objections to Jesus: Theological objections, Michael L. Brow, A Jew who converted to Christianity, Vol. 2, p9, 2000 AD

God created in partnership

Then God said, “Let us make man in our image, after our likeness. -- Genesis 1:26 (ESV)

It is also unlikely that a Jewish Monotheistic religion would copy or translate the text incorrect like this.

Unfortunately the scripture does not name who or what the co-author is or was and what exactly was meant by this verse. So this is open for debate and different interpretations:

The Trinity co-created

Trinitarians reason that at least 2 of the members of the Trinity co-created man.

However, the next verse:

So God created man in his own image, in the image of God he created him. -- Genesis 1:27 (ESV)

If God was a Trinity with 3 personalities, then Adam would have been DID (Dissociative Identity Disorder) and DID would have been the norm for humanity.
If God was a Tritheism God, then he would have created 3 men.
If God was a Binitarian God, then Adam and Eve would probably have been created simultaneously.
If God was an incarnating God, then Adam would have probably incarnated too from one of the animals.
If God was a Kenotic God, then Adam would have probably been a divine being, instead of a human.

God refers to angels

• The most common objection to the “us” in Genesis 1:26 referring to angels is that Scripture attests that God made mankind. But God could easily have headed up a council with whom He conferred, and afterward did the work they decided upon.
• Another objection to this view is that God goes on to say “our image” after saying “let us” so one might question how angels are in the image of God. Since Adam in his pre-fallen state was without sin and in the image of God, it is perfectly reasonable to assume angels in God’s divine council, were also created in the image of God, and without sin. Therefore, it presents no problem to say that humans were created after the image of God (and subsequently angels).

-- Spirit & Truth Fellowship International

Unfortunately this interpretation ignores:

I am the LORD, Who made all things, Who alone stretched out the heavens, Who by Myself spread out the earth; -- Isaiah 44:24 (NRSV)

Misunderstanding

Michael Heiser, a Hebrew scholar, wrote in "The Unseen Realm, p. 39":

The plural of majesty does exist of nouns… but Genesis 1:26 is not about nouns — the issue is the verbal forms.

In other words, God did multiple things and not multiple gods did the same thing.

This could mean that God created multiple people at different times through history.

People make people

Another explanation to consider is that making babies is a co-operative effort between God, male and female.

People do not just appear out of thin air. Even Jesus had a biological mother.

Without God, not matter how hard two partners try, they will not be able to have a baby.
Obviously without either a man or a woman, it is not physically possible to have a baby.

So God could have possibly be talking to mankind in general when He said: "Let us make mankind in our image, after our likeness."

Children also reflect the image of their human parents, often physical but could also show family traits. However, more likely this verse reflect that mankind is supposed to modulate God's dominion over creation.

And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth. -- Genesis 1:26 (ESV)

God doing divine things in partnership

Genesis 3:22

Then the LORD God said, “Behold, the man has become like one of us in knowing good and evil. Now, lest he reach out his hand and take also of the tree of life and eat, and live forever” -- Genesis 3:22 (ESV)

Trinitarians reason that members within the Godhead were having a meeting, however, the next verses reads:

... therefore the LORD God sent him out from the garden of Eden to work the ground from which he was taken. He drove out the man, and at the east of the garden of Eden he placed the cherubim and a flaming sword that turned every way to guard the way to the tree of life. -- Genesis 3:23-24 (ESV)

God was more likely ordering "the cherubim" who was also in partnership with God.

Genesis 11:7

Come, let us go down and there confuse their language, so that they may not understand one another’s speech. -- Genesis 11:7 (ESV)

God as the LORD of hosts was possibly speaking to His angels ("hosts") to "confuse their language".

Singular pronouns

Furthermore, the pronouns in the Bible that refer to “God” are singular, and there are lots of them.

“The Hebrew Bible and the New Testament contain well over twenty thousand pronouns and verbs describing the One God” (Anthony Buzzard and Charles Hunting, The Doctrine of the Trinity: Christianity’s Self-inflicted Wound, International Scholars Publications, New York, 1998, p. 17).

Singular pronouns include “I,” “my,” and “he.”

We would expect that the pronouns that refer to the “Father,” to Jesus, and to “the Holy Spirit” would be singular if there were a Trinity, but since the Trinity teaches that “God” is triune and consists of three “Persons,” that the pronouns associated with “God” would be plural. This is especially the case because according to Trinitarian doctrine, each “Person” in the triune God is individually omnipresent, individually all-knowing; individually all-powerful, and each individually has his own will, his own mind (which is why Jesus could say to the Father, “not my will but yours be done”). John 3:16 (REV) reads,

“For God so loved the world that he gave his only begotten Son, so that whoever believes in him will not perish, but have life in the age to come.”

But if “God” were composed of three co-equal beings who each had their own mind and together agreed to send Christ, we would expect it to say,

“For God so loved the world that they gave the Father’s only begotten Son….”

The fact that the pronouns in the Bible refer to “God” as a singular being is evidence that there is no Trinity.

-- Spirit & Truth Fellowship International

Greek lexicon

Most scholars agrees the Father is God because it is plainly stated in many scriptures. But what about the other members of the godhead?

Comparing the meaning of the Greek words:

For example:

Based on Greek translations of these 2 verses it would mean:

• The Spirit of truth (The Helper): the Spirit of truth is an "extension" of the Father that flow out/spread abroad to the world (John 15:26 NKJV)
• The Son:
  • Jesus was coming from God as a separate individual leaving God behind (John 16:27 NKJV), or
  • Jesus' coming was proclaimed (prophecied) by God