Rooting is giving yourself "superuser" priveleges on your phone. Basically, you hack into your phone to download the "superuser" app. It allows you to use certain applications (such as Titanium Backup and ROM manager) and allows you to download custom ROMs, among other things. It's actually not very hard to do, but make sure you know what you're getting into before you do it.
Virtuous ROM is a custom ROM that's very similar to the stock ROM on the phone. It has a few performance tweaks, some very minor UI changes, and it does away with the "DROID" sound. I've been using it for a while and I'm very pleased with it. I recommend it.
Be advised: before you root, make sure you know how to unroot the phone in case you need to bring it in to a Verizon store. Rooting voids your warranty, so if you bring in a rooted phone for exchange or repair, it won't be accepted.