Christianity, like Judaism and Islam, is monotheistic. That means Christians espouse a belief in only one god. Polytheism is the belief in many gods. Unlike Jews and Muslims, however, Christians believe in a Triune god. This is not three gods, which would be polytheism. It is a belief that there is one God but there are three Persons in that one God. That concept is known as the Trinity. Common sense tells us that 1+1+1=3, so why is this not considered three gods? Well, that same math teaches us that 1x1x1=1. The three Persons of the Holy Trinity are distinct but not separate.
Each has Its own name because each one is a distinct Person: God the Father, God the Son, and God the Holy Spirit. While three Persons, there is only one divine intellect and one divine will, which all three Persons share equally. This means that what the Father knows, the Son and the Spirit know.What one Person wills, all three will.
The Holy Trinity is the greatest mystery of the Christian religion. The monotheistic dogma of one God must be kept intact but so, too, must the revealed truth of three Persons in one God. Some may confuse the Trinity with multiple personalities or with different manifestations or expressions of the same deity. Neither is true.
The Trinity is one God, three Persons: Father, Son, and Holy Spirit. This is why Christians invoke the Holy Trinity every time they bless themselves. Jesus said to baptize “in the name of the Father, and of the Son, and of the Holy Spirit” (Matthew 28:19).
While the human intellect can never fully understand the mystery of the Trinity, for to do so would be to know God as God knows Himself (and then you would be God), our human reason can appreciate some elements of this revealed truth.
The term Father implies an offspring. If God the Father was always God the Father from all eternity and there was never a time when He was not God the Father, then this implies that God the Son always existed from all eternity as well. My dad was a father only after I, his eldest child, was born.While my father preexisted before me, he was not a “father” until he had a son. Likewise, if there was even a second when there was no God the Son, then that would mean there was an instant where there was no God the Father. Fatherhood depends on having children (as does
motherhood). So God the Father is eternally Father, therefore the Son is eternally Son. Sonship also implies parenthood. It is a word which defines a relationship.
Father and son is a relationship. There is no father without a son and no son without a father.
These two persons, Father and Son, are distinct (hence the different names) but they are never separate as they share the same divine nature and essence. Both are equally divine; both are God. The two of them loving each other perfectly and eternally and infinitely, “spirates” the third person, the Holy Spirit. He is the fruit of the love of God the Father and God the Son. Since both exist from all eternity, both love each other from all eternity. The mutual love of these two persons is personified in the Holy Spirit.The Catholic Mass begins and ends with the sign of the cross, where the priest and people bless themselves with their right hands, touching their foreheads, their chest, and their left and then their right breast. While doing so, they say, “In the name of the Father, and of the Son, and of the Holy Spirit.” The priest continues the opening of the Mass with “The grace of Our Lord Jesus Christ, the love of God the Father, and the fellowship of the Holy Spirit be with you all” (2 Corinthians 13:14). This phrase, from Saint Paul, shows that the early Church believed in the Holy Trinity. The Apostles Creed, which goes back to the time of the Apostles (first century AD), and the Nicene Creed of 325 AD, profess a belief in God the Father, Son, and Holy Spirit.
Source: The Catholicism Answer Book by Rev. John Trigilio Jr., Ph.D., Th.D. and Rev. Kenneth D. Brighenti, Ph.D