What is a rooted phone?

Rooting is a term used in Android mobile OS hacking, it provides all the advantages of Jailbreaking (if you're familiar with that) in that you can remove the crap software that the carrier has on by default, make changes to the underlying system code, and even install custom "roms" which can change themes and provide boosts in speed and reliably of the phone. The best website for learning more on rooting your Android powered phone is xda-developers.com