A Deligne-Mumford stack is a space that ``locally has the structure of a
variety modulo a finite group.'' The stackiness comes from remembering
this presentation, in a manner similar to the definition of an
orbifold in usual topology. Many moduli problems are naturally
represented by D-M stacks and not by schemes or varieties (for
instance, they were defined to handle the moduli functor of stable
curves).

Jeffrey Herschel Giansiracusa
2005-06-27