"Yes Virginia, there IS a Santa Claus. He exists as certainly as love and generosity and devotion exist..."His real name was Nicholas, and he lived in the third century in what is now Turkey. He was a Catholic Bishop who was imprisoned for his faith. He saved children and sailors and gave money to the poor. He is the patron and protector of children, virgins, sailors, students, paupers, and all who are in trouble or need. December 6th is the anniversary of his death. The story of how a kindly bishop came to be the fat elf Santa Claus can be seen (literally, with lots of pictures) here.
I like to read my children the book "Santa, Are You For Real." It tells the story of a little boy whose friends tell him that there is no santa, so he goes home and asks his dad about it. His father tells him the story of Saint Nicholas, a very real person who loved Jesus and gave to the poor because he knew it was what Jesus would do. It concludes that stories of Saint Nicholas are told in many cultures, and that he has different names in different places--one of them being Santa Claus--and that when we hear those stories we should remember Jesus and His gifts to us, because that is what Nicholas would have wanted us to remember.
If you would like to learn more about St Nicholas or how his day is celebrated, I recommend visiting the Saint Nicholas Center, which has information about St Nicholas, his history, and modern celebrations around the world. You might also like their subpage the Saint Nicholas Center for Kids (which has stories, games and coloring pages).
Incidentally, if you've ever wondered what the real Nicholas looked like...the image below includes several artists renditions, as well as a modern forensic reconstruction (based on Nicholas' actual scull, which was briefly exhumed during repairs to the crypt where he is buried).