Well, the Trinity is a hard concept for human minds to grasp, something we often encounter when describing God. Saint Patrick probably never used a shamrock to describe the Trinity, but I like to think he did state what the Trinity is when he spoke to two daughters of an Irish King:
St. Patrick, full of the Holy Spirit, responded, “Our God is the God of all, the God of heaven and earth, the God of the seas and rivers, the God of the sun and moon, and all the other planets; the God of the high hills and low valleys; God over heaven, in heaven, and under heaven; and He has a mansion, that is, heaven, and the earth, and the sea, and all things that are in them. He inspireth all things. He quickeneth all things. He enkindleth all things. He giveth light to the sun, and to the moon. He created fountains in the dry land, and placed dry islands in the sea, and stars to minister to the greater lights. He hath a Son, coeternal and coequal with Himself; and the Son is not younger than the Father, nor is the Father older than the Son. And the Holy Ghost breatheth in them. And the Father, and the Son, and the Holy Ghost are not divided. I desire, moreover, to unite you to the Son of the heavenly king, for ye are daughters of an earthly king.
It is enough for us to know that God is a Trinity of Father, Son and Holy Spirit, the mechanics of which will possibly always elude us, but the reality of which we know thanks to what Christ taught us.