In Ireland, St. Stephen’s Day is a national holiday. It falls on Dec. 26, the day after Christmas. Officially, it celebrates the martyr St. Stephen. St. Stephen, says tradition, was stoned to death shortly after the crucifixion of Jesus Christ. There is another legend that says Stephen was hiding in a bush as a wren gave away his presence. Still other stories in Ireland say some Irish soldiers were sneaking up on some Viking raiders when a wren betrayed their presence.
In any event, in Ireland, St. Stephen’s Day is also known as the day of the wren. On St. Stephen’s Day, a group of young men, dressed to look like birds, would parade around the town a dead wren on a stick. They approach various houses asking for a donation. When they accumulate enough money, they hold a party. This custom dates back hundreds of years, perhaps to pre-Christian times. See Irish Central website here for more information.
Another tradition was holding a fox hunt on the day after Christmas. 
The Irish in New Orleans celebrated St. Stephen’s Day the way the Crescent City celebrated most events, they held a fair at the Armory Hall to raise money for the Sisters of Charity Orphanage for young girls. The Irish also held a fair for the building of St. Alphonsus on St. Stephen’s Day. Mass was held on St. Stephen’s Day.
 New Orleans Daily Orleanian, Dec. 27, 1856, p. 1, col. 1
 New Orleans Daily Orleanian, Dec. 25, 1851, p. 2, col. 2; New Orleans Daily True Delta, Dec. 26, 1850, p. 2, col. 2.
 New Orleans Daily Orleanian, Dec. 25, 1856, p. 1, col. 1
 The Louisiana Democrat (Alexandria, Louisiana), Dec. 22, 1880, p. 3, col. 2