When considering the biblical doctrine of the Trinity, we cannot skip over the evidence of John 1:1, "In the beginning was the Logos (Word), and the Logos was with God, and the Logos was God." The importance of this verse for our doctrine of God cannot be overestimated. At least three observations ought to be noted.
1. The use of Genesis 1:1 ought to be glaringly obvious to readers of John's gospel. The famous first verse of scripture reads, "In the beginning God created the heavens and the earth." John's use of this verse indicates that he sees himself as writing a narrative of new creation and that he is going to tell his readers something about the creator God. The chief thing John wants to say about God is that God cannot be known or understood apart from the revelation of the Logos enfleshed in the person of Jesus of Nazareth. If you want to know God, you must know Jesus because Jesus reveals God. John is giving us a Christocentric presentation of his Hebrew understanding of the creator God of Israel.
2. John understands there to be a fundamental unity between the Logos and God. The Logos was God (theos ēn ho logos). This should not surprise us given the fact that, as a Hebrew, John was a thoroughgoing monotheist. He believed there was one God. If the Logos is a divine being for John, then the Logos must be God. There is unity of being between them. Some have argued that the verse ought to be translated: The Logos was a God. The rationale is that since Greek has no indefinite article, and since John does not identify the God to whom he is here referring with a definite article, and since we know its nonsense for God to be both one and more than one all at the same time, then the Logos must be a god rather than the God. For reasons noted above, this argument doesn't hold water. John is Hebrew, remember, and a monotheist. Further, plenty of definite Greek nouns show up without the article. For example, when John writes that those who saw Jesus beheld "glory as of the only born from the Father" (1:14), there is no definite article in front of Father in the Greek text. Surely John didn't mean "glory as the only born of a father." His point is Jesus' unique relation to the God of Israel. It wouldn't help his argument if he were referring to any old undefined father. No, John means the Father in v. 14, and he means the only God in v. 1. The Logos is God.
3. But John does not merely affirm unity between the Logos and the creator God. If he had only affirmed as much, we wouldn't be all that shocked. The surprising thing is that John also says, "the Logos was with God." If John introduces unity between the Logos and God by saying, "the Logos was God," then he introduces diversity by saying, "the Logos was with God." And here is the key issue for John. If we are to understand the true God, we must understand that his nature includes both unity and distinction. He is one and he is more than one (specifically three, as we learn later in the gospel).
The importance of all this for Trinitarian theology is to see that a unitarian approach cannot reckon with this langauge. If God is one being and not three persons, then we have to convieniently ignore John's declaration that the Logos who is God was also with God in the beginning. Neither can one claim exclusive diversity between God and the Logos (and the Spirit for that matter). A tritheistic approach cannot reckon with the langauge of unity between the Logos and the creator God. It is this sort of language that led the Church to adopt the language of "Trinity" to describe the unity and diversity of God revealed in Jesus Christ and in the scriptures. Without the doctrine of the Trinity, there is no account for the biblical language about God. Christianity is a religion of triune theism.
NB: I have avoided the common rendering of "word" for the Greek "logos." "Logos" means much more than the English "word." In order to keep the concept fresh and unrestricted, I've used the transliteration instead.