I am not trying to criticize anyone. But, back when I was a layman, I heard a lot of lame homilies on Trinity Sunday. Who knows? Perhaps by the time we are done here, you will be saying the same thing.
The thing that annoyed me was when the preacher would begin his Trinity Sunday homily by saying something like: “The Trinity is such a mind-boggling, impossible mystery, I simply cannot begin to explain it.” Then he tells you the story about St. Augustine trying to write a book about the Trinity, and the little boy by the sea, and putting all the ocean into one little hole, etc. Okay, okay—we get it. The Trinity is a mystery which surpasses our understanding.
The reason this annoyed me is: The best possible explanation of the mystery of the Holy Trinity is right in front of our noses. The Mass explains the Holy Trinity perfectly. The Holy Trinity is not abstruse, not remote, not unfamiliar. There is, in fact, nothing more familiar than the Trinity for people who go to Mass. Let me explain.
The Lord Jesus taught us to call God our Father. In his letter to the Romans, St. Paul said that, through the Holy Spirit, we cry out, “Abba, Father.” In the prayers of the Mass for Trinity Sunday, we call God our Father eighteen times.
In the gospel, we hear the Lord Jesus say, “The Father has given me all power in heaven and on earth.” From all eternity, the Father has given everything to the Son.
In His bitter Passion, Christ offered everything back to the Father. On the Cross, He said: “Father, into your hands I commend my spirit.”
In the Holy Mass, we enter into this mutual giving of everything, the exchange between the Almighty Father and the divine Son.
It began at the Last Supper, when Christ led the Apostles in giving thanks and praise to the Father. Christ prayed as a priest. At the Holy Mass, we share in this prayer. The whole Person of Christ–Christ the Head and Christ the Body–praises and thanks the Father.
The Fathers of the Second Vatican Council put it this way:
Christ always associates the Church with Himself in the great work in which God is perfectly glorified…The Church calls to her Lord Christ, and through Him she offers worship to the eternal Father.
The Holy Mass is Christ opening up the Trinity and drawing us inside. Here is how the Catechism of the Catholic Church explains it:
In the Sacred Liturgy, the Church, united with Christ in the Holy Spirit, blesses the Father with adoration, praise, and thanksgiving…The Church presents to the Father the offering of His own gifts and begs Him to send the Holy Spirit upon that offering, so that through communion in the death and resurrection of Christ the Priest, by the power of the Spirit, these divine blessings will bring forth the fruits of life to the praise of His glorious grace.
As long as you and I come to the altar in a state of grace, we are united with Christ the Priest in the offering of the Mass. The Trinity is not abstruse. The Trinity is the Father we pray to in the Mass, the Son Who prays in us at Mass, and the Holy Spirit Who helps us to pray as we should at Mass.
It is impossible to list all the different things that the Holy Mass does. But one of them certainly is: It unfolds this mystery of the Holy Trinity for us. And this is enormously helpful, since heaven is nothing other than seeing the glory of the Trinity.
Some of us can say from experience that if you want to run a road race, you have to practice. You practice by running a lot.
The same goes for heaven. If we want to live in the Triune love for all eternity, we have to practice by doing a lot of Trinitarian loving now. By praying the Mass, we exercise this love. The Mass is the perfect exercise to get us into shape for heaven.
In two weeks, Archbishop Wuerl will ordain eight new priests. Right after a bishop ordains a man a priest, he hands the man a paten and chalice with bread and wine, for the priest to use to offer Mass for the first time. As the bishop hands the implements for Mass to the new priest, he admonishes him: “Know what you are doing.” Know what you are doing!
The Lord is saying the same thing to us, dear brothers and sisters. When we go to Mass, we enter into the triune life of God. Christ is opening the door into the Trinity, so that we can step in. He is training us for the unending Mass of heaven.
Father Mark White Blog 
I have long been partial to the analogy of the mind and heart. God knows himself. What God knows is infinite and perfect. While we have fragmented ideas and use many words to express ourselves, God is simple. God has only one idea or one Word which includes all that is. He writes his Word upon human flesh. God becomes Man. The Father or First Person generates from all eternity the Son or Second Person of the Blessed Trinity. Between the Father and the Son is infinite goodwill or Love. That which is infinite is by definition divine. God is Love. The personified Love generated from all eternity between the Father and the Son is the Holy Spirit. God in Jesus Christ becomes a man so that men might share in the divinity, by grace and the restoration of that likeness forfeited by sin. God invites us to participate in his interior life. Making us temples of the Holy Spirit and new Christs, we are invited to share in his Love. The Trinity is our true and final home. The Trinity is very much heaven. The children of God will live within the Trinity forever. I love such reasoning. It also falls far short. The mystery remains. Finite creatures cannot exhaust the truth about an infinite God. We can only scratch at the surface. The Trinity remains what it, or rather, he is, regardless of our participation. God is whole and complete in himself. He does not need us. There was no necessity or compulsion to creation. He did not have to save us. He does so, anyway. Why does God reveal himself, by his fingerprints in creation and by his Son who has entered human history as the Trinity? God wants to establish a relationship with us. He takes the initiative. God always takes the first step. God reveals himself because he wants us to KNOW and to LOVE him. And, even in this return operation or response we find traces of the Trinity.