One repeating Christmas story which is more legendary yet interesting in it's development as 'fact' (through the world-wide web vine) is about the origin of this popular Christmas song. This story is coming from the middle ages that Christmas was extended from a one-day celebration to a 12-day celebration. It begins with Christmas day and ends with the Epiphany twelve days later.
The story of the song develops that during this time period (mid-1500's to the early 1800's) people of the Catholic faith were being repressed by laws in England. To hide their Christianity but teach their faith, believers came up with a song that was a catechism for children to learn the Catholic faith, and each of the gifts were a clue to this.
Some believe the meaning of the song is as follows:
Others believe the song was simply a delightful rhyme set to music. The song was developed and used as a "memory and forfeits game" that was played by the children of this time period. The game was played by a leader reciting the first verse, and continued around, each child reciting the next verse.
Many Christians do celebrate January 6 as the Epiphany, also known as the 12th Day of Christmas, the Twelfth Night, Three King's Day. The word epiphany means an appearance or manifestation especially of a divine being; an illuminating discovery as when the Magi finally found the baby Jesus.
Note that this story does not have "hard evidence" as to the true nature of the song and is more likely anecdotal. It can certainly be used today to teach a part of Christianity. We repeat this story because it is a fun song to learn as well as other Christmas-related songs - no matter what your faith.