ok, so how do you root and what makes it so important?
HOW TO:Root, Install Clockwork, Remove Bloatware, Integrate Google, Un-root, and more - xda-developers
that is the one stop shop for how to root, what you can remove, installing recovery etc.
basically if you are happy with your phone and dont want any future panic-y moments then you dont need to root
that being said....root allows you to do A LOT that you normally can't do to your phone. you can use custom kernels which are smoother, faster, and use less battery than the awful stock samsung one. some kernels have backlight notifications built in which substitute for the lack of led notifier
you can use free wireless tether (well u dont need to root to do this, but ud have to buy pda net for 10 bucks or something)
you can theme the entire phone (status bar, fonts, icons, etc)
you can freeze/remove unwanted bloatware from samsung/verizion
you can remove ads from free games and the browser
you can take screenshots without the sdk (ok this is kinda misleading because shootme works w/o root on our phones for some weird reason)
you can put leaked os/custom roms on your phone which increase the functionality of the phone
and a lot more though