MUSH stands for Multi-user Shared Hallucination or Multi-user Shared Hack and MUD stands for Multi-user Dungeon.
Basically, these are old textbased play by post style games that were sort of like text-based MMO or Massive Multi-player Online games.
This is a drastic simplification but think World of Warcraft but text-based with descriptions of location that are given to you when you travelled from room to room to talk with other players.
Huh, sounds a bit neat although it also sounds like it could get confusing: How would you remember where you were when you went out exploring, and how would you find your way back?
Well that's what you get a Navigation skill for. =P