Nicholas of Myra was a Christian Bishop in Asia Minor that lived in the late third and early fourth century. He was one of the attendees at the Council of Nicaea, so had a hand in shaping the Nicene Creed.
He reportedly placed money in the stockings of poor girls that had been left to dry overnight, so that they could pay their dowries.
He was a very popular saint, and due to his gift-giving, came to be associated with such a tradition. This was on 6 December, his feast day.
Now the Magi brought gifts to Jesus, traditionally celebrated on Epiphany (6 January) which is why gifts are often given on this date in many countries, like Russia. These two usages got confused in the popular imagination.
Mediaeval Christmas ballooned into a 12 day feast, as in the 12 days of Christmas of the song, from 25 December (Christmas day) to 6 January (Epiphany). Gift-giving thus migrated from the end of Christmas to its start. Thus Nicholas found himself giving gifts on Christmas.
Now the name Santa Claus is derived from the Dutch for Saint Nicholas, Sinter Klaas, which is itself a corruption and folk etymology from Saint Nicolaus.
I am sure the venerable old saint is spinning in his reliquary about the commercialisation of Christmas, but I doubt he would be opposed to the gift-giving or family-centredness of the modern holiday.