The advantages of rooting have been covered before, and with rooting comes flashing ROMs and mods to your device. The easiest method for flashing anything is to do it through recovery.
Recovery is the bootable portion of the phone's system that allows data wipes and system updates. At its core, the stock recovery is fairly limited in the functions they can perform. This is where custom recoveries come in to play.
A custom recovery will allow you to flash ROMs, mods, themes, etc. You can also back up your entire system, partition internal and external memory, wipe various parts of your device... more