Rooting is the Android equivalent of jailbreaking, a means of unlocking the operating system so you can install unapproved (by Google) apps, update the OS, replace the firmware, overclock (or underclock) the processor, customize just about anything, and so on.
Of course, for the average user, rooting sounds like -- and can be -- a scary process. After all, "rooting" around in your smartphone's core software might seem like a recipe for disaster. One wrong move and you could end up with bricked handset.