Christmas Carol: the First Noel Josh Groban feat. Faith Hill

Please see The Carols We Love: The "Story Behind the Story of Twenty-two Classic Christmas Carols, Daniel Partner, Barbour Publishing, Uhrichsville, OH, 2002.
This is a traditional English carol from the early renaissance period.  In this case Noel refers to the birth of Christ.  It is a word which means birth from Latin.  It is capitalized because it only refers to the birth of Jesus Christ.