Carols were originally Pagan songs sung during the Winter Solstice celebration and were used for dancing. In 129, a Bishop wrote a carol for Christmas which would replace the Pagan version of carols. It was to be sung during Christmas Mass, as Christmas was slowly creeping in and replacing the Pagan celebrations of Yule, Saturalia, and other holidays associated with the Winter Solstice. Other Bishops would follow in this suit and began to write Christmas carols to be sung as well, and songs that would eventually be sung during Advent and Epiphany as well.
Carols were song at "mystery plays" in the 1000's, plays that told a story. These particular ones often depicted the Nativity, the Annunciation, or the Visitation of the Magi, among other stories. In 1647, Puritans took over England as the major religion, and due to their discouragement of celebrating Christmas for its Pagan origins and singing, carols were stopped for a time. Additionally, Calvinists discouraged the use of carols and the celebration of Christmas early on due to the strong ties it had with Catholicism.
Carols were often still sung in secret, and in other coutnries such as Italy. Eventually, Puritans began to lose power as religious freedom began to surface in Great Britain, and carols were once again sung. Many Americans also sung carols. There was a surge in popularity of then during the 18th and 19th century.
Modern carols have been written as well, many of which are secular. These days, a carol can be defined as either a hymn that is intended to be sung during Advent, Christmas, and Epiphany, or Christmas song that has reached "legendary status."