St. Patrick's Day was originally a Roman Catholic holiday celebrating Ireland's patron saint and observed only in Ireland; it was not until the 1700's when Irish immigrants in the U.S. started the first St. Patrick's Day Parade in New York City.
The March 17th tradition of wearing green is explained in differing ways. It's said that blue was originally the color associated with the holiday but over time green took over in popularity due to Ireland's nickname as "The Emerald Isle", the green in the Irish flag and the clover that St. Patrick used in his teachings about Catholicism.
In Ireland, some still follow the tradition where Catholics wear green and Protestants wear orange. These colors are associated with the religious sects and are the represented on the Irish flag; the white on the flag is symbolic of the peace between the two.
On the holiday, people in Ireland do not wear as much green or celebrate quite as wildly as revelers do elsewhere, although there is a legend that wearing green makes you invisible to leprechauns that will pinch you if they can see you.