Here are a few facts about the Twelve Days of Christmas (and the song). This is by no means and exhaustive list.

But first, did you know the twelve days of Christmas begins, not ends, on December 25th. December 25th begins the Christmas season, not ends it. The Christmas season lasts those whole 12 days.

Shakespeare’s play Twelfth Night was set during Twelfth Night.

Twelfth Night is the night before Epiphany, January 6th, the day celebrated as the day the Magi (wise men, three kings) found Jesus and gave him his gifts of gold, frankincense, and myrrh (one for his Kingship, one for his Lordship, and one for his death on the tree).

Twelfth Night parties are the first of the feasts during the time of Carnival or Mardi Gras, a time of fattening (more on this latter)

In the song we sing “calling birds” but originally it was “colly birds” which is an old generic name for a blackbird.

The song is a list of collective presents, not comprehensive. So on the first day of Christmas the true love gives a partridge in a pear tree. On the second day of Christmas the true love gives two turtle doves and a partridge in a pear tree. By the end of the song the recipient has been given:
twelve (12 x 1) drummers drumming
twenty-two (11 x 2) pipers piping
thirty (10 x 3) lords a-leaping
thirty-six (9 x 4) ladies dancing
forty (8 x 5) maids a-milking
forty-two (7 x 6) swans a-swimming
forty-two (6 x 7) geese a-laying
forty (5 x 8) gold rings
thirty-six (4 x 9) colly birds
thirty (3 x 10) French hens
twenty-two (2 x 11) turtle doves
twelve (1 x 12) partridges in pear trees

As you can see, the next little fact is that the song makes a palindrome.

There’s more, but those are a few favorites of mine.