How to understand the Trinity
The Holy Trinity (God being three Persons but one God, distinct but indivisible) is one of the central mysteries of our faith -- and in some ways the hardest to understand, because it goes to the depths of the mystery of Who God is -- which our human minds can only grasp in limited ways.
It's very hard to depict in art -- but of course Christian artists have tried in many ways over the years, such as in the traditional depiction above of Jesus the Son of God seated by the right hand of God the Father (depicted as an old man holding the orb [the world] in his hand) and the Holy Spirit depicted as a dove hovering between them.
For those who prefer the "lesson plan" approach, The Catechism of the Catholic Church has a very good section to help us understand God the Holy Trinity. I recommend reading and studying that, because it is impossible to try to communicate that in a 10-minute homily! Plus, it has footnotes and references for further reading, if you really want to delve into it.
At Mass, we do more than learn about Who God the Holy Trinity is, we share in the love of the Trinity in the most powerful way possible on earth. That's because God (the Trinity) is love: the source of all love, communicated to us through Jesus the Word of God in the Holy Spirit.
Ultimately, we have to use our minds to learn about the Holy Trinity, open our hearts to His love, and then turn our will to respond in obedience and love to His love. The Trinity affects our whole person -- right down to the core. And that's because we have the Trinity "stamped into us" at our baptism, when we are snatched from the grip of Satan and claimed for God, the Father, Son and Holy Spirit.
This is so important that the Church recognizes only baptisms made under that formula: "I baptize you in the name of the Father and the Son and the Holy Spirit." But that's a topic for another day.