Christmas celebrates the Incarnation, or of God "becoming flesh" with the birth of the second person of the Trinity - Jesus. For many Christmas day is seen as the "end" of a hectic period of shopping, sending out cards and decorating in preparation for the holiday. Though it's true that Christmas day is December 25th, it is only the beginning of the liturgical season of Christmas in the church.
So how long is the Christmas season? Traditionally the Christmas season ended on the Feast of the Epiphany, traditionally January 6th (in the United States Epiphany is celebrated on the Sunday between January 2 and 8). The song "Twelve Days of Christmas" references this period. We'll come back to Epiphany in the next paragraph. The liturgical season of Christmas begins with the vigil Masses on Christmas Eve and concludes on the Feast of the Baptism of the Lord (celebrated on the Sunday after Epiphany). This day commemorates Jesus' baptism in the Jordan River by John the Baptist.
Epiphany, from the Greek verb meaning "to reveal", commemorates the three magi arriving with their gifts of gold, frankincense, and myrrh. These were very specific gifts with meaning behind them. Gold was an appropriate gift to honor a king, and used in honoring God. Frankincense was an important ingredient in incense (Exodus 30:23, 34), and myrrh was the key ingredient in the oil used to anoint priests as well as prophets. These gifts recognized Jesus as prophet, the eternal High Priest and King.
To access some great resources for the Christmas season, including an interactive calendar from the USCCB, click here.