A Nandroid backup is a backup of your phone that is an exact image of the state of your phone. So you could make an exact copy of your current phone, then do major changes to it, and then restore to your previous backup by flashing the backup back to the phone. Flashing means to copy or to install.... you are essentially wiping the device and restoring a previous state (a backup) or you are flashing a new ROM (which is a custom version of Android).
More info: I've rooted my phone. Now what? What do I gain from rooting?, What is the difference between: Rooting, Jailbreak, ROM, Mod, etc.? , etc.