Advantages essentially would be ad-free experience, titanium backup (allows you to backup EVERYTHING), flashing a rom (basically take a stock rom and adding some tweaks to make it better), a new kernel (its the thing that allows your software to interact with your hardware - improves battery life and performance) - this also allows this cool thing known as voodoo sound and colours. What this means is your sound experience during a movie, video or music is much better than a stock experience as well your colours of the screen can be tweaked to POP and by pop I mean it becomes so much more richer and lastly you get tweaks such a battery percentage icon, new boot animation, etc. The easiest way to root would be going to xda - nexus s - general - there is a thread on a easy one click root method. Hope this helps!