The custom of giving presents goes back to the ancient Romans. In the Bible, the Wise Men brought gifts to Jesus on the twelth day after his birth, so in some countries, children receive their presents not on Christmas Day, but twelve days later, exactly.

In some northern European nations, gifts are exchanged almost three weeks before Christmas. The reason for this is that the gifts are supposed to be brought by Saint Nicholas on the eve of his feast day, December the sixth. Saint Nicholas was a bishop during the fourth century who came to be regarded as a special friend of children. So, in countries such as Holland, Belgium, Switzerland and Austria, and in parts of Germany, Saint Nicholas returns with presents for good children.
When the Dutch came to New York they brought these traditions with them. They called him San Nicolaas, which was soon changed to Sankt Claus, which later became Santa Claus.