Christmastide has always been a time for gift-giving. While most think this references the gifts of the Magi to the infant Jesus, gift-giving at New Year's was already an established custom started by the Romans. "Strenae," sweet cakes and small trinkets like thimbles and needles, were the usual gifts.
In some of the northern countries, St. Nicholas was the gift giver and arrived on the eve of his saint's day, December 6. Due to the gifts received by Jesus and connected with his birth, the most common gift day is December 25.
But in many of the warm countries, the gift-giving day is the feast of the Epiphany, when Biblical record tells us the Magi found Jesus, His mother Mary, and His foster father Joseph. The nativity story is actually in two parts. The one which Linus quotes in A Charlie Brown Christmas is from Luke, which tells of the journey to Bethlehem, the angels announcing the birth to the shepherds, and the visit of the shepherds themselves.
The visit of the Magi, or Wise Men (or "kings," although the Bible never says they are royal), occurs in Matthew, and does not happen concurrently with the birth/shepherd story (as has been presented in many stories, including Rankin-Bass' iconic Little Drummer Boy). Matthew, in fact, states that Jesus and his family are not in a stable, but in a house, and that Jesus is a small child, not an infant. The number of Magi is not mentioned either; they are usually numbered at three because of the three gifts mentioned. There could have been more gifts: the gold, frankincense and myrrh were symbolic of Jesus' kingship, priesthood, and death.
The gift givers vary by country. Most Spanish-speaking countries are given gifts by the three "kings." In Syria, the gift-bringer is actually the smallest camel in the kings' caravan.
Both Italy and Russia have a twist on this story. Italy's traditional gift-giver is La Befana, although most modern Italian kids ask for gifts from "Babbo Natale," their version of Santa Claus. "Befana" is a corruption of "Epifania." The Russian version is named "Babouscka." She is usually portrayed as looking a bit like a kindly Hallowe'en witch, with tattered clothing and old shoes because she has been traveling for so long.
So the story goes, elderly Befana, like most traditional Italian women, was cleaning her house. The three kings stopped at her house for directions. After offhandedly pointing the way out to them, Befana is in a hurry to get back to her cleaning. They ask her if she does not want to come with them to see the infant King. No, no, she says, I have to finish my cleaning.
The kings leave (in some versions of the story, she misleads them, but the star shows them the true route) and Befana finishes her cleaning. She now feels guilty, gathers up gifts for the new little King, and hurries after them. But she never catches up with them. Instead she visits every home where there could be a child, and, not knowing if this is the correct one, leaves a gift. (Sounds a bit like the Flying Dutchman...)
The feast of the Epiphany officially ends Christmastide. Some legends say all greens and decorations should be out of the house by this date. However, Candlemas (February 2) is known as the last day for the burning of the Christmas greens.
In Norway, the official ending of the Christmas season is January 13, St. Knut's Day.