The nature of the trinity is a mystery, one of the most difficult things to understand in the Christian faith. The simple fact of the matter is that no one can explain it because it defies our comprehension. The best that we can hope for is some sort of analogy that helps us to understand. Even in analogy, however, there is the danger of communicating what is not true about God along with what is helpful in the picture.
What we do know is that the Bible teaches both that there is one God and that the Father, the Son, and the Holy Spirit are all that God. We cannot fully comprehend how these things work together, but orthodox Christians typically attach the phrase “one God in three persons” or say that the Father, Son, and Spirit are “of the same substance.” What all this means is that we believe that there is one God, but that He is revealed in three distinct persons.