The term the "Trinity" was first used by the early church Father Tertulian, who attempted to provide a succinct term for the tri-unity that existed in God. Simply put this is a term that articulates there is one God, who exists as three distinct persons: the Father, THE Son, and the Holy spirit. Each are fully God and equally God.
The Bible is clear from beginning to end there is one God. Deut 32:39- "There is no God besides me". (etc...Isa 43:1, 45:5, 1 Tim 1:17, 1 Tim 2:5). This notion has always existed as countercultural in our polytheistic world. It is today, it was on the Day that Abraham left Mesapotamian Ur, and on the day that Paul showed up in Athens in Acts 17. There has always existed a plethora of false "gods" that are worshipped by our world. Regardless Christendom has alwasy heralded that there is but one God, the God of the Bible. Now the doctrine of the Trinity is historically what theologians have use to articulate two truths, the first being that there is one God. And the Second being that this God is comprised of Father, Son, and Holy Spirit.
The 3 Persons each as God:
-God the father is God: no need to be belabored simply because few would deny this point. (But John 6:27, 1 Cor. 8:6 "There is one God the father")
-Jesus is God: more debated. John 1 "In the beginning was the word, and the word was with God, and the Word was God...and the Word became flesh and came to dwell among us", John 8:58 "Before Abraham was I am" (etc... John 20:28, Romans 9:5, Titus 2:13, 1 John 5:20.)
Holy Spirit is God. The spirit is a person not a force. He is personal not impersonal. He is responsible for convicting, instructing, teaching, guiding, and enlightening us. He can be grieved and resisted (to an extent). 2 cor 3: The Lord is the spirit and where the spirit of the Lord is there is freedom...this comes form the Lord who is the Spirit." (etc...John 4, Acts 5).
1 John 4:8- "God is love", in the very essence and Nature of God there exists a triplicate relation of Love. The trinity brilliantly manifests this truth. Trinitarian Doctrine clearly denies the idea that God could have possibly fashioned the universe out a desire for company. The God of the bible has never had any needs that finite man could possibly meet (Acts 17). But rather the universe was spun into motion by what Jonathan Edwards coined "an overflow of love" pouring out into creation magnificently.
Old Testament evidence for the Trinity.
"In the Beginning God created the heavens and the earth...and the Spirit of God was hovering over the face of the deep."Genesis 1:1-2 (In the first 2 lines of the scripture we see distinct doctrine of parts of the trinity, i.e. the word for God here is Elohim and plural word for the Hebrew God "El". We also see the presents of the Holy spirit working his part in creation).
Further evidence from Old Testament Jewish beliefs of the trinity. The Targum Neofiti- 200BC. (A targum is an accepted interpretation of the Scriptures from a Rabbi-- similar to a modernday commentary.) This specific Targum states that "In the beginning by the firstborn, God created the heavens and the earth. Now the earth was formless and void and the spirit of God was hovering over the face of the Deep." - This was 200 years prior to the birth of Christ! There existed at least to a certain extent Jews who were waiting for the coming messiah they believed to be God the son. Now not all Jews may have bought into this but clearly it was by no means a revolutionarily new idea from the 1st century AD Church.
Now why this is so important? Because it is a central tenet of not only Christian orthodoxy, but of the Nature of God. To deny such a principle is to deny a portion of God. It is the beauty and mystery of the trinity that magnifies that sacrifice of the Cross. Had Jesus simply been a creation of God (And not God, like Jehovah's witness, Islam, and Mormonism would all claim) then his sacrifice would be no more noble than that of any other altruistic sacrifice that have taken place throughout the history. (Men dying to save their country, families, faith. Or women dying to save their children...etc All are noteworthy but not monumentally and profoundly altering to the fabric of life, like Christ's sacrifice on the cross was.)
This is why the term used by members of Islam "people of the book", which they use to unify all Jews, Musilm's, and Christians together because we all worship the same God and trace our beliefs back to Father Abraham is faulty. We as believers in Christ believe neither in the God of the Muslims nor the God of the Jews. Because both of these sects fail to recognize Jesus as both our savior and our God. There is one God to deny that Christ is God is to deny God.
This Triune existence does not however operate in a fashion that resembles that of the metamorphic phases of Water. (i.e. liquid, ice, steam). God fully exists (well beyond human comprehension) in 3 distinct persons as one distinct God head. We see them working together throughout and within creation. Thus the economic trinity works in history for the redemptive plan of Salvation, but not in some limited Modalism that would require him to act in one mode discontinuous from the other two modes. Simply put God plays all 3 roles in a simultaneous fashion(Modalism is a teaching in the modern-day Pentacostal church that teaches God works in one mode at a time not in all three at all times, although this is perhaps not quite heretical it is without question not biblical. Matt:3: clearly portrays at Jesus's baptism that all three persons were present and evident).
The Trinity is a crucial belief that all of Christianity rises and falls upon. To deny this belief is to deny the faith in its totality. But it is important to remind ourselves that the "Trinity" is in no way a new idea, and not a creation of man. Rather man is a creation of the "Trinity" and its beautiful overflow of love in the creation of the Universe. The doctrine of the Trinity is an incredibly important component of our faith. We live in a world that is constantly attempting to pervert Biblical Christianity and tempt it to conform to the more unitarian beliefs of the dying world around it. If this doctrine is not understood, defended, and proclaimed Christendom will only move further towards impotency and heresy.
---God preserve your bride, and cause her to flourish for the Glory of your name.