Unrooted is a stock out of the box device, Rooted means you have full control over your device (you can make it do things the manufacturer didn't want it to do). A few examples would be wireless tethering, taking "screenshots" adding themes, and flashing ROM's
A ROM is basically someone else's (A DEV...or developer's) interpretation of the Android O/S...these days most ROM's are built from Source (the ground up) and can include a lot of things the Original O/S didn't include, Custom Kernels (make your CPU run faster) Custom Scripts (make tweaking your device easier) Custom Boot Animations...and an overall better Android Experience