Some MUDs are combat-oriented games; imaginary players fight imaginary monsters (or other players) with imaginary weapons. Other MUDs are socially-oriented, allowing players to interact with each other. About the only theme that virtually all MUDs share is the "spacial metaphor"; that is, MUDs' interfaces are organized around some rudimentary model of a virtual reality. Players are able to look at each others' characters and their surroundings, move from room to room, and perhaps even build their own rooms.
A good source of information about muds is the MUD Frequently-Asked Questions List, available here.