I know MUD stands for Multi-User Dungeon, but what exactly does that mean? I've also heard that all MUD's are text-based; is this true?

MUD's are (as far as I know) all text based. A mud is basically a text based rpg - commonly online. The user creates an account and then moves around a text based world. The most common solution for this is to have rooms with exits that join to other rooms. Other solutions exist however, where a small ASCII map is displayed, and users move around this way.

MUDs also have the advantage of having less limits. Because it is all text, the features can go on a lot (I suggest taking a look at www.achaea.com - there is an insane amount of role playing in that, more than a graphical game could ever hope to achieve - at this time of writing).

I hope this clears things up. I believe wikipedia will have some info on this topic too.

Thanks for clearing that up for me, I may try my hand at writing one ;)