December 6 is the Feast of Saint Nicholas of Myra, a bishop from the fourth century. He is, of course, the model for our modern-day Santa Claus, because Saint Nicholas's generosity was legendary. His generosity continued even after his death, through the many miracles (especially of healing) attributed to Saint Nicholas's intercession.
Saint Nicholas's charity was bound up with his firm orthodoxy, and it is said that, at the Council of Nicea in 325, he walked across the room to the heretic Arius, who denied the divinity of Christ, and slapped him in the face. It's hard to imagine our "right jolly old elf" doing that!
Saint Nicholas is the patron saint of the Byzantine Catholic Church, and his feast day is very important to Eastern Catholics and Eastern Orthodox. Positioned about halfway between the start of Philip's Fast--the Eastern Christian time of preparation that coincides with Advent--and Christmas, the Feast of Saint Nicholas provides some relief from the austerity of this "little Lent."
The night before Saint Nicholas Day, children place their shoes in a prominent location--say, by a fireplace, or outside their bedroom door. The next morning--usually very early--the children find their shoes filled with little presents from the great saint.
Like many Advent customs, the celebration of Saint Nicholas Day reminds us that Advent is a time of preparation for the birth of Christ. The love of Saint Nicholas, while great, pales in comparison with the love that Christ has for all of mankind.