Well first off you picked a bad time to feel like a IT geek cause the DX cant be rooted yet. But it should come somewhere down the road as the bootloader is cracked
Rooting short and sweet lets you do things with your phone that were previously not included or locked out, and also to make the phone more "yours"
With rooting you can:
Apply Custom Themes (colors, text, boot animations, icons, etc)
Use app's that weren't native to your phone
Overclock (speed up the cpu so the phone is snapier)
Custom Roms (These roms could be newer leaked versions of Android, (like we are experiencing now with 2.2 official release just over the horizon) or just modified stock Android Roms with new features to also customize the phone to "YOU"
Free Wifi Tethering (free usage though your data plan instead of paying the 20-30 bucks extra a month for it from Verizon (dunno how this will play out after the data plan teir's are put into effect.
As far as bad things? There really isnt anything outside of "Bricking" your phone. Now on a Moto Droid thats basically impossible. But it wont be known how possible or hard it is to brick the DX until someone cracks the bootloader. But if the sbf file is leaked (and it prob will be) for the DX it will be just as hard, if not basically impossible, to brick the device
There it is in short, anything else just ask