Why do people give each other presents on Christmas day?
The tradition of gifts seems to have started with the gifts that the wise men (the Magi) brought to Jesus. As recounted in the Bible's book of Matthew, "On coming to the house they saw the child with his mother Mary, and they bowed down and worshipped him. Then they opened their treasures and presented him with gifts of gold and of incense and of myrrh."

As mentioned in the previous question, however, no one was really in the habit of exchanging elaborate gifts until late in the 1800s. The Santa Claus story (described later), combined with an amazing retailing phenomenon that has grown since the turn of the century, has made gift giving a central focus of the Christmas tradition.