Trinity (or Tri-unity) is the word Christians use to refer to what God reveals about Who He is.
The doctrine of the Trinity is a mystery that we do not fully understand. What God reveals about Himself in this regard in the Bible requires that we hold to three truths:
God is three Persons.
Each Person is fully God.
There is one God.
We cannot explain how these three statements can fit together, but if we do away with or weaken any one of them we are not remaining consistent with the truth that the Bible clearly teaches.
Because God is three Persons, then the Father, the Son, and the Holy Spirit are each distinct Persons. The Father is not the Holy Spirit and the Holy Spirit is not the Son.
It is not possible to be God, as each of the Persons is, except to be fully God. This is so because God is infinite.
(Spotlight 8, Lesson 3 in Doctrine 101: Learning about God)