This is a term that cannot be found anywhere in the Bible. It is a theological term used to describe a teaching which is derived from several passages in the Bible in both the Old and New Testaments.
It really says: THREE-UNITY This term refers to the fact that God, who really is one (in essence) has made Himself known (revealed Himself) to us in three ways.

When you get to know a person, you can tell somebody what he is like. We learn what God is like in three Persons:

-God the Father

-God the Son

-God the Holy Spirit.

Eph 3:9
And to make all see what is the fellowship of the mystery, which from the beginning of the ages has been hidden in God who created all things through Jesus Christ.

Gen 1:26
And God said, Let US make man in OUR image, after OUR likeness...

Gen. 1:2
And the Spirit of God moved upon the face of the waters.

Although the Lord Jesus and the Holy Spirit are revealed to us in our final understanding in the New Testament, it is clear to us that all three Persons of the Godhead were present from before time began.

GOD IS ONE

Deut 6:4
Hear, O Israel: The Lord our God, the Lord is one!

This was the specific message that came to Israel in a world that worshipped many false gods and idols and does not conflict with the N.T. teaching of the Trinity.
God is not an absolute unity, but rather a compound unity. We read about man and wife who shall be one flesh (Gen 2:24) and how a whole nation can act as one man...

Judges 20:11
So all the men of Israel were gathered against the city, united together as one man.

The word ONE used in these verses is a different word as used to convey absolute oneness. Deut 6:4 uses the plural Name of God ELOHIM. This shows us that although God reveals Himself to us in three persons, He is inherently ONE SPIRIT, indivisible in component parts, numerically one, free from composition.

The New Testament teaches this truth with the same clarity:
James 2:19

You believe that there is One God. You do well. Even the demons believe that - and tremble!

In the New Testament, God revealed that He is not only one, but a family of persons - an eternal, inexhaustible, and dinamic triune family of Father, Son, and Holy Spirit, who are one in will and purpose, love and righteousness.

THE TRINITY DEFINED:

In order to clearly understand that the Godhead is a Trinity in a Unity, we must not stress either the threeness or the oneness to the point where we fall into Tritheism (believing in three Gods) or forgetting the distinction of Persons (Sebellianism - that Father, Son and Holy Spirit are merely three aspects of manifestations of God)

From before time began, before any creature existed, there was an eternal fellowship between the three distinct Persons of the Godhead - every One of Whom was God, and was conscious of the other Two. Therefore there could also be a manifestation of the existence of LOVE. Otherwise, one could reason, how could God be Love - since God doesnt change?

1 John 4:16
And we have known and believed the love that God has for us. God is love, and he who abides in love abides in God, and God in him.

GOD IS LOVE FROM BEFORE ETERNITY.

The three Persons operate in singleness of mind and purpose, so that we can say that They are truly one:

-The Father CREATES

-The Son REDEEMS

-The Holy Spirit SANCTIFIES

In each work we see all three PRESENT. The Son and Holy Spirit co-operate in the creative work. The Father and the Spirit sent the Son to redeem. The Father and Son co-operate in the sanctifying work of the Spirit.

For the work of man's redemption, the Son entered the world in a new way when in New Testament He took upon Himself human nature. He was given a new Name - Jesus. At Pentecost, the Holy Spirit entered the world in a new way as the Spirit of Christ, being embodied in the Church, which is made up of all individual believers. We see that:

-The Father testified of the Son (Matt 3:17)
-The Son testified of the Father (John 5:19)
-The Son testified of the Spirit (John 14:26]
-The Spirit testified of the Son (John 15:26)

THE WORD TRINITY:

Although the word trinity is not in the Bible, it was used as early as 181 AD (Greek:Trias) and by Tertullian in 220 AD (Latin: Trinitas). The trinitarian formula is mentioned in the Great Commission (Matt 28:19) and in the benediction of the apostle Paul's second Epistle in the Corinthians (2 Cor 13:14)

In the Christian theology, the term TRINITY means that there are three eternal distinctions in One Divine Essence (being). These eternal distinctions are known as:

-Father
-Son
-Holy Spirit

The doctrine of the trinity means that within the being and activity of one God, there are these three distinct persons.

THE ATHANASIAN CREED:

A fixed formula to summarize the articles of Christian religion is called a creed, and carries the authorization of the whole Church. It is thoroughly based on Scripture, the result of hundreds of years of discussions amd an*lyses of the Word. It is more specific than just JESUS IS LORD or a benediction:
2 Cor 13:14
The Grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Spirit be with you all. Amen.

Athanasius (4th Century) said:

We worship one God in the Trinity, and the Trinity in unity;
we distinguish among the persons, but we do not divide the substance.
The entire three Persons are co-eternal and coequal with One another, so that...we worship complete unity in Trinity and Trinity in unity.

This is the great mystery of God - His glory can not be measured

EXPLANATION BY ILLUSTRATION

For a better understanding, we may look at nature and human personality.

Nature

- Water appears in three forms - fluid, solid (ice) and gas (steam)

- Fire brings forth heat, light and fumes [smoke]

The Sun's rays are invisible, but when blocked, give light and heat (known to scientists as actinic, luminiferous and calorific)

- A triangle has three sides and angles yet one surface and one shape.

Human Personality

- Man is one -
Yet consists of
-spirit
- soul
- body

Indication by Paul's Letters:

Paul gave a subtle indication of his trinitarian view by the way he organized some of his writing. part of Romans is outlined as follows:

-Judgement of God upon all flesh (Rom 1:18 - 3:20)

-Justification through Faith (Rom 3:21 - 8:1)

- New Life in the Spirit (Rom 8:2-30)

We find a similar pattern in Galatians:

- Justification through Faith (Gal 3:1-29)

- Adoption into sonship (Gal 4:1-7)

- Christ makes free from the law (Gal 4:8 - 5:15)

- New Life in the Spirit (Gal 5:16 - 6:10)

When we think of God, we obviously cannot have more than a fraction of an idea of What, How and Who He is. But we should always be aware of the multiplicity of His personality, the immensity of the variety of the aspects of His character and the vastness of the gap between what we understand Who He really is.

YOU
DO
NOT
NEED
TO
UNDERSTAND
A MYSTERY
TO
AKNOWLEDGE
IT.

SHADOWS AND REVELATION

When studying the Bible, one is astounded again and again by the unity of the book as a whole: the Old Testament will point to something while the New Testament outlines it clearly. what is only a shadow of a truth becomes the revealed light.

It is quite a relief to discover that what we learn about the doctrine of the Trinity could only be known by revelation through the Scriptures. Let us have a look at the Old and New Testaments in turn.

OLD TESTAMENT SHADOWS:

We have already mentioned the plural form of the Name of God, ELOHIM. Although this could be so for the purpose of intensity, it must have made an impression on the Hebrew speaker whenever he heard or uttered this name, that there is a plurality of persons in the one God. Because of the worship of many gods in the world around them, the Israelites had to be taught first that God Elohim is one God. The accent was clearly on this truth. Certain verses, however, point to a trinity.

Psalm 2:7
I will declare the decree: the LORD has said to Me, You are My Son, today I have begotten you.

Isaiah 48:16
Come near to Me, hear this: I have not spoken in secret from the beginning; from the time that it was, I was there. And now the Lord GOD and His Spirit has sent Me.

Isaiah 63:9
In all their affliction He was afflicted, and the Angel of His presence saved them; in His love and in His pity He redeemed them; and He bore them and carried them all the days of old.
From these verses we see the Son and the Father are distinguished.

Gen. 1:1
In the beginning GOD created.. And the SPIRIT of GOD was hovering over the face of the waters.

Gen 6:3
And the LORD said, My SPIRIT shall not strive with man forever.
Psalm 51:11
Do not cast me away from Presence, and do not take your HOLY SPIRIT from me.
Isaiah 40:13
Who has directed the Spirit of the Lord, or as His counsellor has taught Him?

From these verses we see the Spirit and God (the Father) are distinguished.

THE TRIPLE USE OF HOLY:

Isaiah 6:3
And one cried to another and said: HOLY, HOLY, HOLY is the LORD of hosts; the whole earth is full of His glory!

THE TRIPLE BENEDICTION:

Numbers 6:24-26
The LORD bless you and keep you;
The LORD make His face shine upon you, and be gracious to you;
the LORD lift up His countenance upon you, and give you peace.

THE ANGEL OF THE LORD

This phrase is often found when one of the O.T. characters met up with God in person. This was a foreshadowing of the second person of the Godhead coming in the flesh. He was a messenger and yet spoke with godly authority in the first person. See Genesis 22:11,12