Based on the three leafed clover that abounds in Ireland, it's cultural significance goes all the way back to St. Patrick and is uniquely tied with him as the symbol of Ireland.
Even prior to the arrival of Christianity, it was believed that the number 3 was a perfect number and had inherent mystical powers. No one is quite sure why they believed this but it is possible the number signified totality – past, present and future. The Celts attached great significance to the number and this is clearly expressed in their artistic symbolism.
St. Patrick, when he set out to convert the Celtic inhabitants of Ireland, used the significance of the number three, and, according to legend, he used the plant to illustrate the Christian concept of the Trinity.