The word "Trinity" does not appear anywhere in the Bible; yet it is an accepted element of Christian belief, that is that God has a Triune (three in one) existence. It is best explained in the Bible Encyclopedia as follows:
There is one only and true God, but in the unity of the Godhead there are three coeternal and coequal persons, the same in substance but difference in subsistence. ...The doctrine of the Trinity is a revealed doctrine. That is to say it embodies a truth which has never been discovered and is undiscoverable by natural reason.
As with many tenants of Christianity, it is a doctrine that is accepted without proof, but is accepted purely as a matter of faith. It is one of those elements of the religion that is accepted as true without truth or explanation.
The word "trinity" does not occur in the Bible. The idea of the trinity has a basis in the Bible, but the actual term itself does not appear in the Bible.
The idea of the trinity does clearly show up in the Bible. For example, in Matthew Chapter 28 Verse 19, Jesus is telling his disciples (this is after the Resurrection) to go and convert people. He tells them that they should go out and baptize people in the name of the Father and of the Son and of the Holy Spirit.
So, in this verse, we clearly see an example of where the concept of the trinity comes from. The verse refers to all three parts of the trinity and puts them in a context that implies that they are all equal parts of the Godhead. However, the word "trinity" does not appear.
If you read in the book of Genesis 1:26 you will see that the scripture refers to God as being more than one. It says, "let us make man in our image, after our likeness." This doesn't indicate polytheism, it is a reference about the trinity. There is also more evidence throughout the Bible that confirms the existence of God the father, God the son, and God the holy spirit.