Here's the thing-- you have to remember that the Trinity is not really meant to be understood. It's one of the concepts of God that we as humans cannot understand because it is beyond our comprehension. Once you accept this, it is easier to discuss.
The Holy Trinity usually refers to God, Jesus and the Holy Spirit. They are also called the Triune God ('Triune' means 'three in one'). The basic idea here is that they are three distinct "Persons" (for lack of a better word), but they are also one God. It is important to realize that this does NOT mean that there are three Gods. God is God. Jesus is God. The Holy Spirit is God. God is Jesus is the Holy Spirit. Distinct and individual, but the same. 3 = 1. Three Persons. One God.
Logically and mathematically, this does not really make sense. But this is God we're talking about. We are unable to make sense of God with our human minds.
For an in-depth explanation, check out this article.