St. Patrick is the patron saint of Ireland. He was a priest or a monk who came to Ireland around 1000 AD to spread Christianity. Mythology states that with his staff he drove the snakes form Ireland into the sea. Since there are and never were any snakes native to Ireland this is likely an analogy for his attempt to drive out the indigenous (pagan) religions and replace them with Catholicism. (After the Ice Age, reptiles moved back north into Europe but by then the ice bridge connecting Ireland with England was gone. Only the viviparous lizard made it across the bridge and is the the only native reptile on the island. The waters are too cold for other reptiles to swim across.)
St, Patrick is often pictured with a shamrock (a type of clover) whose three leaves he taught symbolized the religious trinity of God, Jesus, and Holy Spirit.
Symbols common to Victorian and Edwardian era St. Patrick's Day cards are the shamrock, the Irish harp or lyre once part of the Irish national flag, the phrase "Erin Go Bragh" and the color green which was also part of the Irish flag and is gaelic for "Ireland Forever". Leprechauns and their pots of gold are also featured as part of St. Patrick's Day symbology and Irish mythology. Leprechauns are sprites that can grant you wishes if you can catch them which is very difficult to do.