Gifting during Christmas is believed to be a pagan ritual (winter solstice) that became associated with Christmas recently. This ritual was practiced in ancient Rome in December, with gift giving during the Saturnalia holiday.
As Christianity grew in this region, the custom of gift giving as carried on. Christmas was fixed on the Saturnalia in order for the people to readily embrace the tradition of celebrating the birth of Jesus Christ and also continue the tradition of exchange of gifts.
But in our world today, a new interpretation has been given to this act, giving and receiving gifts is done to remind Christians of the presents given to Jesus at his birth by the wise Men.