It gives you full control of your device. For instance, all apps that come preinstalled on those devices can not be uninstalled. If you have root access to your device you can do with them what you please.
Out of the box you only have guest privileges which means that operating system is locked down so that you can't modify it. Root access gives you administrator privileges so that you can manipulate those system files however you desire.
The catch is that it can be risky if you don't know what you're doing, and that's why it's important to do research beforehand and ask as many questions as you need to to make sure you're doing it right. In all honesty, it's not actually that risky if you follow the directions to a T. Most of the time if something goes wrong it can be fixed. That's the beauty of Android. It's actually pretty difficult to break the device beyond repair while doing these things. We call this a brick...because at that point it's as good as a brick. Plus, brick just sounds cooler than paperweight, lol.
*Sent from work early bcuz some1 4got teh NSFW tag*