The phrase "Twelfth Night" refers to the Church calendar and the last night of the twelve days following Christmas Day, December 25th. The Twelfth Night falls on January 5th or 6th, depending on tradition. The Twelfth Night is also the eve of Epiphany, which celebrates the Magi bringing gifts to baby Jesus. The Twelfth Night was also full of festivities. While one might think the festivities would have been related to the birth of Jesus, apparently the parties in Shakespeare's time could get quite wild.
Shakespeare wrote the play Twelfth Night; or What You Will for an Epiphany Eve party held at "one of the Inns of Court in 1602," a party that can be described as "absolutely secular and even quite bawdy" ("Shakespeare's Twelfth Night"). The party "was a time of masques, revels, defiance of authority, and general foolishness" ("Shakespeare's Twelfth Night"). Hence, the reason why, despite the title, Twelfth Night contains no Christmas content is because the celebration on Twelfth Night, or Epiphany Eve really had nothing to do with Christmas. Instead, just like the party the play was written for, the play explores loss of innocence, foolery, revelry, deception, and a general festive atmosphere.