Have you ever wondered: "why is it that December has two major holidays that we celebrate both on the evening before, and the day of?" Of course I am referring to Christmas Eve and New Year's Eve. Well, the answer is that a new day used to start in the evening rather than at midnight. This is why celebrations related to a day (like Christmas, New Years or Epiphany) often began on the evening before the actual day.
Christmas Eve, therefore, used to be the start to the festival season of Christmas, which ran through the New Year until the Feast of the Epiphany on January 6. The evening before Epiphany (January 5) is called Twelfth Night because it is the twelfth night counting from the evening of December 25. Since we measure our days differently today, the First Day of Christmas is generally thought to be December 26 and, accordingly, the Twelfth Day of Christmas falls on January 6. The last six days of the old year bridge to the first six days of the New Year during the Twelve Days of Christmas.
If you want to read more about Christmas Eve, and the tradition of a day starting the evening before, you can head over to Wikipedia.