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.