The shamrock was chosen Ireland’s national emblem because of the legend that St. Patrick had used it to illustrate the doctrine of the Trinity. The Trinity is the idea that God is really three-in-one: The Father, The Son and The Holy Spirit.
Patrick demonstrated the meaning of the Three-in-One by picking a shamrock from the grass growing at his feet and showing it to his listeners. He told them that just as the shamrock is one leaf with three parts, God is one entity with three Persons
The shamrock had been seen as sacred in the pre-Christian days in Ireland. Due to its green color and overall shape, many viewed it as representing rebirth and eternal life. Three was a sacred number in the pagan religion and there were a number of “Triple Goddesses” in ancient Ireland, including Brigid, Ériu, and the Morrigan. (text from “An ode to St Patrick’s Day -Apanache (https://apanache.wordpress.com/2014/03/17/stpatricksday/)
Happy St Patriçk’s Day!