A MUSH ("multi-user shared hallucination") is a type of mud which is often used for social and role-playing activities. It is derived from "Tinymud", an early mud server. Its distinguishing features are that any player can typically extend the virtual world by building new rooms and objects, and its internal programming language, MUSHcode, which is considered to be fairly easy to learn.
PennMUSH is one of the most popular and actively developed MUSH codebases.
The "Flagship" PennMUSH mush is M*U*S*H, at: http://mush.pennmush.org.