The concept of gift-giving at Christmas time originated with the gift-giving of the three kings or Magi, to which they are sometimes referred. Their three gifts were gold, frankincense (simply, incense) and myrrh.
Gold was the traditional metal of royalty and signifies the kingship of Christ. (Frank)incense for centuries has been used in religious services, as a prayer to deities. It signifies the divinity of Christ. Myrrh was a burial ointment. It signifies that Christ was human and suffered death.
In my ancestral country of Italy, gifts are passed out by La Beffana (meaning Epiphany), a female form of Santa Claus on the 6th of January.
This is just one example of the richness of religious customs throughout the world and in every religion. It is good to keep the old customs relevant for all time.