ok here is the short answer. basically, the typical modified xbox is akin to back in the day when you used to have to unlock a processor to gain access to the higher multipliers. it essentially "unlocks" your xbox to more of a role of a regular computer or media center pc. there are many various advantages anywhere from using modified and homebrew games to running linux on it, but i would say that the main reasons that people mod their xbox is so that they can run games off of the hard drive and so they can watch divx movies on their television. running games off the hard drive is one of the greatest advantages in my mind. i always forget just how slowly games load when playing off of the disc until i have to. but basically, you are running games at hard drive speeds rather than at dvd rom (and shitty dvd drives at that, cept for some of the later samsungs). it really just makes everything better all around. and as far as a media center pc goes, i would much rather have an xbox. the vast majority of xbox's run evolution X which is basically just an operating system that allows you to manage the settings, programs, and games that you have on your xbox. for media files, most people use XBMP (Xbox Media Player) or XBMC (Xbox Media Center). XBMP used to be the standard for the xbox, but XMBC is the more popular one nowadays because XBMP used locked media player 9 code that could not be modified, so XBMP is fully open source. anyway, evolution x (also called evox or evo-x for short) automatically sets up an ftp server on your xbox so that you can transfer files and folders over with ease. this allows you to upload your divx or xvid (or pretty much any codec you can think of. occasionally i will need a new codec for my pc, but i have never found a file that wont play on XBMC) to your movies folder and then simply browse and play. in addition, these players have enhancements that often times will make your divx movies appear better on the xbox than they would on my pc (mainly because of the clarity of lcd's, but still

). in any event, there are tons of useful applications to be found. one of the really exciting communitys is the homebrew community for xbox. they focus on both coding new games for play on the xbox and modifying existing games for xbox. you can get all your favorite older pc games for play with a controller if you want such as doom, rise of the triad, duke nukem, and quake 2. quake 2 plays better than it ever did and it has full networking capabilities and can even run a quake 2 server for you right off of your xbox. anyway, thats enough about that, if you have any questions let us know.
in the meantime, maybe some of us folks can get together and start an official xbox modding thread and we can throw in all the collective knowledge that folks have and then we can toss together a general article about it . . .