The Christmas season in Italy goes from the beginning of advent to the twelfth day after Christmas, roughly 5-6 weeks. Santa Claus, or Babbo Natale (Father Christmas), might bring a few small gifts to children on Christmas Eve, but the big gifts are on Epiphany Eve and are from La Befana, the good witch. The Epiphany celebrates the arrival of Three Kings in Bethlehem to see the newborn Jesus on January 6th.
The story goes like this: La Befana has been an Italian tradition since the XIII century. She was approached by the Three Wise Men who asked her to lead them to the stable where the baby Jesus lay in a manger. La Befana was too busy cleaning her house at the time, so she declined the offer to go with them. Very soon she realized her mistake, and she collected a bag full of gifts and set off alone in search of the baby Jesus. She was unable to find the stable, but she continues to search the world for the Christ child one house at a time. Good children are rewarded with candy and gifts. Naughty children are supposed to get coal, but it is more likely that they will find some rock candy made of black sugar. After all, she is a nice witch.