After Jesus when the celebration of Christmas was only just started, Christmas was more of a gathering and a mass mashed into one. Unlike today, giving gifts or receiving gifts was another symbol, like the star of Bethlehem, and was a rare practice.
Some other symbols were used during Christmas such as Holly or Ivy which showed someones understanding and grieving. Others showed their commitment and others someones own sacrifice. Symbols such as gifts are more modern and were shown as to praise the birth of Jesus.
