Rooting gives you the user access to system files, this means you can modify them. You can run root only apps like Titanium Backup, Root Explorer & AdFree.
Rooting also allows you to install a custom recovery like CWM or TWRP with which you can flash custom kernels like the new over clock kernel which will over clock the CPU to I think 1.6GHz and you can flash custom ROM's like Cyanogen Mod 10.