rooting is to an android...as chipping is to a ps3...as jailbreaking is to an iphone
what this allows you to do is to load a custom rom image instead of the stock/oem provided one. these are versions of android os that are coded to look different, add different enchancements or to provide better performance or battery life.
some features you might get depending on what rom/kernel you use:
-use your phones data plan and tether to devices via wifi or usb free
-new menu layouts
-ability to theme easily
-custom music players with support for lyrics
-new camera controls
-quick controls on notification pulldown (bt/wifi/brightness/sound/etc)
-data watcher with warning or shutoff (so you dont go over your limit)
-audio equalizer
-many more
i'm currently running the MIUI rom ver 1.11.25 and its GREAT. the only issue i've seen is that connecting to a network wifi kind of sucks since it will not autosearch (yet) but using your phone as a wifi broadcaster device works great and is found by your laptop/other device without issues.
by rooting you do void your warranty but i believe there are ways now of unrooting so that you can send a phone in for service. also rooting is a much much simpler process now and with programs like titanium-backup and rom-manager its very hard to brick (make the device not work) a phone unless you really screw up bigtime.
i've been using an android device for a little over a year and i've tried quite a few different things. i'm also one of the active posters on this subject here.
if you want app suggestions, rom suggestions, or just plain android suggestions give me a private message and i'll get back to you when i can.