1. More Options
By rooting you open your phone up to customs roms that allows your phone to have better speed along with better keyboards and the ability to back up your entire phone.
2. Better Performance
You can overclock your devices CPU to gain the most speed. Be careful as overclocking can damage and overheat your device.
3. Applications
There are thousands of applications that don't made for rooted devices such as emulators and software tweaks such as the capability of turning your phone into a hot spot.
4. Remove blotware
Sometimes your phone comes loaded with unwanted software that you can't remove and wastes valuable space. With a rooted phone you can finally remove the unwanted carrier software.
5. Increase internal storage
With a rooted phone you are able increase storage and install more applications.