Patrick was an English boy who was kidnapped and taken to Ireland as a slave back in the 6th century (or thereabouts). Some years later he escaped and went back to England where he was educated. Since he had grown to love the country and people of Ireland he went back there as a missionary to teach the pagan Irish about Christianity. As he tried to teach the difficult concept of the Holy Trinity to the people he used an easily available tool to teach about the three Gods in one Godhead. He picked up a shamrock which grows everywhere in Ireland and shows the three leaves making one leaf on the plant as a visible tool to teach the people which they could readily understand. This symbol of a shamrock is now used as a symbol of St. Patrick, but his original use was the shamrock as a symbol of the Holy Trinity.
As well as converting Ireland to Christianity, St. Patrick is also remembered as removing all snakes from Ireland and is now of course the Patron Saint of the country.