BBC Radio 4 has had a series of programmes on the history and origin of the Christmas carol recently. I only heard a trailer and not the programmes themselves, but they did sound as if they'd be interesting (the tail end of them can be heard for a few more days here, and there are other clips on the page).
A Christmas carol is a song relating to the Nativity these days, but the original sense of the word, when it entered Middle English from Old French, was a ring-dance, or merry-making involving dancing. It soon came to mean a song, and in particular, according to the OED, "a song, originally that to which they danced".
As the OED says, "The ulterior etymology of Old French carole and its accompanying verb caroler, is uncertain". It's likely to be related to the Greek-Latin chorus. Another conjecture is that it comes from the Latin corolla, little crown or coronet, which would link it to the dancing ring. Another early meaning of carol, believed by some to be the original sense, was a ring, particularly of standing stones. Another old name for Stonehenge is Carol, or Giants' Carol, and also Giants' Dance (chorea gigantum).
Merry Christmas, everybody. I'll be back in a few days.