Many MUDs (especially in the LPMUD family) have some features that are clearly derived from roleplaying games: Newbies start weak, fight monsters, gain experience points, rise in power. When players reach a certain level, they attain Wizard status. They are allowed to modify the game. See MultiUserSharedHallucination for a slightly different approach.
As to the game itself, players find themselves in rooms. Players are objects that receive commands from a telnet connection. Other objects include weapons and tools that allow new commands. Rooms are actually also just objects that have connections to each other. So in the end, you can have objects that can be entered. In the end, rooms, players, and objects are all the same: They have a description, they have relations (inside another object, connecting to other objects).
Players interact whenever they are in the same room. You talk, the others hear you. They talk back. Since just "saying" things is hard, you can also "pose" -- describe what your character does instead of what he says. It turns into collaborative story writing.
One way to view this is as a complex information retrieval system. The rooms are like documents, they have content. They link to other rooms. There global commands, local commands, there are command tools, there is interaction with other users. It is pretty powerful.