YES, what it reminds us of is that we need to reflect and channel the very Trinitarian life of God in our own life. That means that just as in God there are three persons who are perpetually engaged in perfect knowing and loving, we too should try our best to know and love God and everybody else all our life the way God knows and loves himself and all his creation, especially us.

Obviously, in our case, this perpetual process of knowing and loving will have a beginning, but it is supposed to end up by being carried up in the perpetual knowing and loving of God in heaven. Here on earth, we should just try our best to live that process as far as we can.
And the way to do that is to follow what Christ himself told us as the new commandment we need to live, and that is to love one another as he himself has loved us. Following that new commandment of Christ would necessarily link us in a living way to God the Father and the God the Holy Spirit in the way Christ is linked with these two other persons in the Trinitarian God.

If we truly follow Christ’s commandment, then we would have the same sentiment that God in his Trinitarian life has towards us. Or said in another way, we can only follow Christ’s commandment if we have the same sentiment God in his Trinitarian life has towards us.
And what is that divine sentiment? We are clearly told about it in the gospel of this Solemnity of the Most Holy Trinity that this year falls on June 4. (cfr. Jn 3,16-18)
“God so loved the world that he gave his only-begotten Son, so that everyone who believes in him might not perish but might have eternal life,” the gospel says. “For God did not send his Son into the world to condemn the world, but that the world might be saved through him.”

We as persons are patterned after the Trinitarian persons of God. Like God, we have to know God and everybody else, as far as we can, the way God the Father knows himself and everybody else.

We should try that our knowledge of God and of everybody and everything else should be as perfect as God knows himself and everybody else. This perfect divine knowledge is personified in God the Son, who as God who became man offers us the “way, the truth and the life.”

We have to be properly known the way God the Son, the pattern of our humanity, is known perfectly by the Father. In other words, our knowledge of God and everybody else should go as faithfully as possible as the knowledge God has of himself and of everybody and everything else—a knowledge that is personified in the Son.

And we have to love God and everybody else the way God loves himself and everybody and everything else, as personified in the Holy Spirit. This is what Trinity Sunday in the end reminds us of.

In the above-cited gospel, we are told that only when we believe in Christ, “the way, the truth and the life” for us, can we avoid condemnation. (cfr. Jn 3,18) And believing in Christ precisely involves the process of knowing and loving God the way Christ knows and loves God and everybody else. Only then can we reflect and channel God’s Trinitarian life in our life.