A Christmas carol is a carol about Christmas-y stuff that is usually sung around Christmas time. In the 12th century a monk started using ideas from popular music to make something close to Christmas carols, but English versions of more popular carols were to be found in 15th century compilations. Well-known Christmas carols today include Jingle Bells, Rudolph, the Red-Nosed Reindeer, and Joy to the World.
From Wikimedia Commons: This Endris Night, a fifteenth-century English carol performed by the chorus of U.S. Army Band "Pershing's Own". Link