Dec. 6 is the Feast of St. Nicholas of Bari, a Saint in the Catholic pantheon who lived between 270 A.D. and 346 A.D. in modern day Turkey. He rose to the position of Bishop and was famed for giving gifts from his sizable inheritance to better the lives of his flock. His two most famous acts involved saving three girls from being sold into prostiution by donating their dowry and bringing back to life three children who had been butured by an inkeeper. Get Medieval has the whole story. You can also find an extensive treatment of the Saint's life in the Catholic Encyclopedia.
Since his cannonization as a Saint in the early church, feasts of St. Nicholas have long been associated with the giving of gifts. Not surprisingly then, this long, two millenium old tradition has evolved through today, where we commonly refer to St. Nicholas of Bari as . . . Santa Claus
Update: For some very good videos on the history of Chirstmas, please see my post here.