The Catechism of the Catholic Church (CCC) has much to say about the central mystery of our faith: The Holy Trinity. When we bless ourselves we are invoking the Holy Trinity. CCC 234 states (in part): “The mystery of the Most Holy Trinity is the central mystery of Christian faith and life. It is the mystery of God in himself……”
God has one nature, but is actually three persons. Just as you and I are a person and we have a human nature, God the father is a person and has a divine nature. God the Son is a person with the same divine nature, and God the Holy Spirit is a person with the same divine nature.
It might help to think of it this way: God being all loving and all knowing and the creator of all things, is Love itself. Love needs an object right? So perhaps think of the object of God’s love being His son, Jesus. We say in the creed that Jesus was “Begotten, not made”. God’s Love begat an object of His Love: His Son. Jesus, of course, loves His Father. And the Love that exists between the two of them, is an actual third person: The Holy Spirit.
Three distinct persons, One Divine nature. None of them possess anything the other does not. If one did, that would mean the others were somehow limited and could ‘grow’ and attain something they do not already possess.
CCC 237 states (in part) The Trinity is a mystery of faith in the strict sense, one of the “mysteries that are hidden in God, which can never be known unless they are revealed by God”……..His inmost Being as Holy Trinity is a mystery that is inaccessible to reason alone……
To read more about the Dogma of The Holy Trinity see CCC, especially Part One.