Santa Claus, or Father Christmas, has his origins in the 4th century AD. St Nicholas was Bishop of Myra in southern Turkey, and among his good deeds he gave bags of gold to three poor girls so they could marry. This is why he is particularly associated with giving gifts to children.
In some countries in the northern Europe, children were given presents on December 5th, the eve of St Nicholas's Day. When Dutch migrants arrived in New York, this was mixed with Scandinavian tradition of giving children a lump of coal or a gift according to whether they had been naughty or nice. The Dutch name San Nicholas changed to Sankt Klaus and eventually to Santa Claus.
In different countries, gifts were given on other days: Christmas Day itself or January 6th to commemorate the gifts of the biblical Three Kings. Eventually, all three traditions became mixed up presents are now mostly given around December 25th.
The Santa Claus Origins
In England we moved the date of Santa's arrival to Christmas Eve. Gradually his red costume, the reindeer, and his home at the North Pole became part of the tradition.