Mumming is a word for disguising oneself, going door to door, and performing songs, dances and plays in neighbour's homes and in public places. It's a very old and widespread custom, going back at least to the Middle Ages.
The type of play we call a Mummers Play today is a little less ancient and less universal. In fact, it may not go back any further than the 18th century, since earlier English-language references to "mumming" either are vague about the exact type of performance, or are clearly a different kind of play.
Modern Mummers Plays have a basic recurring plot that is used as an excuse for the actors to sing, dance and rhyme. The plot involves a fight between two champions, who can be St. George and the Dragon, or St. Patrick and the Turkish Knight, or any other combination of historical or fantasy characters.