Rooting is simply changing the attributes of the root directory of the phone to allow you to modify, delete or copy files...including system files. Once you have those attributes to read and write you can put custom ROMs or over clock kernels on the phone. ROMs are mostly eye candy menu systems with more home screens or fancy colors. Some come with pre-ported apps that would not have been available on your phone when you bought it, but you don't need the ROM to get those ported apps. It simply puts in all in one box to make things simpler. Before 2.1 was released a lot of people wanted multi touch and the new picture gallery we would eventually get with 2.1 so the custom roms added those apps.
Root access allows you to also run apps like wifi tether so you don't have to download an app from the market to tether the phone to your computer and share internet access. With the WiFi tether apps we can create a hot spot where multiple laptops can log into your phone's internet access as an ad hoc network. Can't do that without root access.
If you root, it is up to you to be careful and not delete any neccesary system files. That is why Vz voids your warranty. They are not going to be held responsible for you screwing up the operating system. The good news is we can do the needed repairs ourselves once we are rooted. Vz just won't hold your hand. To date I have not seen a single phone discussed that the Rescue Squad (Look in the Hacks forum) can't help you fix.
I paid extra for the extra warranty and I kind of wish I did not now that I know how durrable and easy to fix these phone are. But at the end of the day....if I need that warranty I can always put this thing back to factory specs in about 20 minutes and get it taken care of. I don't know if Vz cares so much that I rooted...they just don't want it back in their hands if it is still rooted. If I unroot and it is still broke then it is a problem with the phone...not something I caused by rooting. Since the law says that warranties can't be voided simply because someone installed an aftermarket part, they have to prove that the aftermarket part caused the failure...I feel perfectly comfortable challenging them in court. That of course assumes that what we think is a safe process turns out to be safe. These phones are so new no one can say for sure rooting is safe and does not cause long term damage. So you will see all the disclaimers on the developers posts...not responsible if you brick your phone. And I am certianly not telling you you should root. I am simply answering your question so you can do your own research and decide for yourself.
Good luck
Nate