Carols are Yuletide songs which are usually narrative and celebratory in nature with a simple spirit and often in verse form (I've posted a list of some of my favorites over on the Eleventary Blog). The term carol has a varied and interesting past and is derived from several words that include the idea of dancing as well as singing.
It has been often mentioned that the first carol was sung by the Angels to the shepherds on the night of Christ's birth. Mary's song, the Magnificat, could also fit in the category of early Christmas music.
The idea of caroling from one home to another seems to have started sometime during the 18th century or earlier. Carolers would visit each house of a parish on Christmas Night to sing songs of the Nativity and to call forth blessings on every home. The term wassail means "Good health!" Carolers would often receive food, money, and drink--as thanks for the spreading of good cheer.