A lot of things!
First of all, it's not jailbreaking. while it can be confused with jailbreaking an itouch/iphone because they produce *somewhat* similar outcomes, it is different than on android. Android can do most of the things that a jailbroken apple device can do without any modification. For android, we call it "rooting." Rooting is the process of opening the locked folders in the android system, allowing us to edit, add, and delete things that are not meant to be. Essentially, it's like switching from a "Guest" account to an "Administrator" account. It also allows for flashing custom roms, which can greatly improve performance and visual appeal (This is something that idevices can not, for the most part, do.)
But what's so great about rooting?
1. make system changes as you see fit (Overclocking, themes, etc.)
2. run apps that require special permissions (E.g. screenshot apps)
3. custom roms! This is my favorite because i can tell you firsthand that it has made my mytouch 4g WAY better. More visually appealing, better battery life, and i got android 2.3 before an update was officially released!
I hope i answered your question!