I think the practice of Christmas Caroling came from visiting one’s neighbors and wishing them well in hopes of receiving a gift from them. It developed into singing Christmas songs in public, usually going door to door through a neighborhood, or visiting a mall or nursing home and singing Christmas songs. I don’t see this nearly as much as I did when I was growing up. Christmas Caroling is a fantastic way to evangelize and lift people’s spirits. It’s a great community builder and it leaves lasting positive memories for children.
I was surprised to see there is actually a WikiHow for this, so here it is: http://www.wikihow.com/Go-Christmas-Caroling