They don't really need to be converted, but due to the Xbox's limited memory, and different features, not all mods will work. Luckily though some of the best ones do though! (Better bodies, better heads)
The "conversion" process in a nutshell (same as on PC actually):
copy the folder in the meshes folder in the zip to the Data Files\Meshes folder.
copy the folder in the textures folder in the zip to the Data Files\Textures folder.
put the esm file in the Data Files folder.
You also don't necessarily need a modded system. If you use the MechAssault save to FTP into your xbox after Morrowind has been run, you can copy mods straight to the Data Files folder on a cache partition (the X, Y, or Z folders). Then, reboot and pop in your Morrowind DVD and enjoy playing with the mods! If you don't like em, either wipe the cache folder via FTP or play a few other games, which will eventually write over the cache morrowind used, and it will regenerate the original files from scratch next time you play.
Anyways, the above two mods will make your base Morrowind look much better and as such are recommended, but there are plenty others. There are also Xbox compatibility listings for mods (search the forum). <