"Carol" is a derivative of the French word caroller, the interpretation of which means dancing around in a circle. Carol and carols, eventually came to mean not only to dance, but included music and lyrics - hence Christmas Caroling.
Christmas carols are based on Christian lyrics and relate mostly to the Nativity. Christmas carols were introduced in to church services by St Francis of Assisi in the 12th century.
The joyous themes for many traditional Christmas carols were banned in England by the staunch Protestant Oliver Cromwell and many of the very old Christmas carols and songs were subsequently lost for all time. They were only fully popularized again during the Victorian era when they again expressed joyful and merry themes in their carol lyrics as opposed to the normal somber, Christian lyrics found in hymns. As religious observances in the United States and England were closely linked, the popularity of Christmas carols grew in both countries during the 19th century. Many Christmas songs are relatively recent, and bear no relation to Christmas carols, such as the famous 'Grandma got run over by a reindeer'.