First MS blocked the JTAG hack in August of 2009 so chances are you can not do it to your 360. If you should buy one though the short version is it blows your 360 wide open.
It allows you to run your own code on the 360 (although there is not that much- certainly not as much as the original xbox and not even up there with the wii) but in addition to this people made hacked versions of the dashboards allowing you to run hacked games, ignore ping limit patches (system link over the internet- you can even host on a stock machine), hack the original xbox emulator (attempt to run your xbox code of your choosing regardless of whether it is signed or not), remap controller buttons, run XBLA and DLC, install games to the hard drive (extracted or as a GOD install), run things from plain USB (no need to "format" a USB drive for it), install whatever size hard drive you want, access 360 hard drives via FTP and probably a bunch more I am forgetting but those cover the main things you can do.
You still need to flash the DVD drive if you want to run copied discs (although with a JTAG machine it will spit the numbers at you or you can figure them out which is the hardest part of DVD flashing on the 360) and you lose the ability to play over xbox live but that is about it.
