The word 'trinity' comes from the word 'tri' meaning 'three' and 'unity' meaning 'one'. Catholics believe that there are three distinct Persons to this one God and that these three Persons form a unity. This belief is called the doctrine of the Trinity: God the Father - the creator and sustainer of all things.
The Trinity, Three Persons in One God, is a community of love. All are equal. Each has a special mission: The Father creates; the Son redeems, the Holy Spirit guides. Through Baptism we become members of the Trinity. We, too, are called to love on another through our special mission/vocation as Christians.