We all probably know that Santa Claus is named after Saint Nicholas, but from there the story gets a little blurry. Saint Nicholas was a real person who lived in the area we now know as Turkey. Bishop Nicholas was born around 280 A.D. to a wealthy set of parents who died when Nicholas was young. Bishop Nicholas used his wealth to help others by giving them gifts, a large percentage of which were children. One story of Bishop Nicholas generosity revolves around his giving money to a family for dowries for three daughters so they could be wed rather than be sold into slavery or prostitution.
After his death around the years 345 A.D. and 352 A.D., Bishop Nicholas eventually became Saint Nicholas with his feast day being celebrated on December 6th of each year. Because of the generosity of Saint Nicholas during his life, it became a custom to give presents during the celebration of his feast day. The tradition spread and the Dutch shortened Sint Nikolaas (Dutch for Saint Nicholas) to Sinter Klaas.
Around 1530, the legend and traditions of Saint Nicholas became less popular and Martin Luther pushed to have gifts given in the name of the Christ Child, Christkindl, on Christmas Eve. Martin Luther loved Christmas and wanted the season to focus on giving in honor of the supreme gift Christ gave us. With the legend of Saint Nicholas becoming less popular, in the U.K. gifts became to be given by Father Christmas or Old Man Christmas.
Over the years the names evolved. Sinter Klaas became Santa Claus and in America Christkindl became Kris Kringle. Through all these changes the tradition of giving gifts continued, it simply shifted from December 6th to Christmas. From this one can see that the legend of Santa Claus is truly an international development.
The jolly old elf that we think of today in the red suit with white trim came later. A lot of this had to do with the marketing of Christmas by the shops selling gifts for Christmas. History becomes what is written today, and this is my version of history based on three different, although similar, accounts. If you want to read more, here are the links:
Santa Claus
St. Nicholas, Santa Claus & Father Christmas
Saint Nicholas and the Origins of Santa Claus