The doctrine of the Trinity means that there is one God who eternally exists as three distinct Persons — the Father, Son, and Holy Spirit. Stated differently, God is one in essence and three in person. These definitions express three crucial truths: (1) the Father, Son, and Holy Spirit are distinct Persons, (2) each Person is fully God, (3) there is only one God.
The fact that the Father, Son, and Holy Spirit are distinct Persons means, in other words, that the Father is not the Son, the Son is not the Holy Spirit, and the Holy Spirit is not the Father. Jesus is God, but he is not the Father or the Holy Spirit. The Holy Spirit is God, but he is not the Son or the Father. They are different Persons, not three different ways of looking at God.
The doctrine of the Trinity does not divide God into three parts. The Bible is clear that all three Persons are each one-hundred-percent God. The Father, Son, and Holy Spirit are each fully God. For example, Colossians 2:9 says of Christ, “in him all the fullness of deity dwells in bodily form.” We should not think of God as a “pie” cut into three pieces, each piece representing a Person. This would make each Person less than fully God and thus not God at all. Rather, “the being of each Person is equal to the whole being of God” (Grudem, Systematic Theology, 1994, page 255). The divine essence is not something that is divided between the three persons, but is fully in all three persons without being divided into “parts.”