A simplified expalnation from Brewer's:

Mumping Day.

St. Thomas's Day, December 21. A day on which the poor used to go about begging, or, as it was called, "going a-gooding," that is, getting gifts to procure good things for Christmas (mump, to beg).   
    In Warwickshire the term used was "going a-corning," i.e. getting gifts of corn. In Staffordshire the custom is spoken of simply as "a-gooding." (See MUMPERS.)