It means we take control of what is installed on the phone. Along with that action the cellular provider will not support our phone any longer so this may be an issue for those that want the support for their phone.
For most, rooting a phone is not needed. Mine is not rooted and I see little reason to do so.
http://en.wikipedia.org/wiki/Rooting_%28Android_OS%29 covers this very well. It agrees that we do this to gain privileged control over the phone.
In simple terms, let's say that Sprint set the phone to disallow us to remove some apps. Rooting it can let us remove said app but at the price of losing support.
Know how to save a wet phone?
It's not with a dryer and it's not with rice. CNET shows you the secret to saving your phone.