These days, we tend to think of the "Twelve Days of Christmas" as simply a Christmas song with overly annoying refrain ("and a partridge in a pair tree..."). But in fact many ancient and modern Christians celebrate the time period between December 25 and January 6 (The Feast of the Epiphany) as an extension of the holiday. Some consider it to be representative of the trip of the Wise Men (who did not visit Jesus in the manger, but some time later) and others simply a time of joy. During this time, "some celebrants give gifts each of the twelve days, feast and otherwise celebrate. Lighting a candle for each day, and of course, singing the appropriate verses of the song each day are a part of modern-day American celebrations. Some still celebrate Twelfth Night as the biggest night for parties and gift-giving. Epiphany morning is then the traditional time to take down the Christmas tree and decorations."
(Source Wikipedia and The Catholic Encyclopedia)