(It's The Roots, get it?)
So you want to know about rooting your Android phone, eh? Yeah, it sounds a little scary. It's kind of a big leap, and it may involve a few steps. and quite possibly the use of a command prompt, which would require you to follow instructions and type words and stuff.
Here's rooting in a nutshell: Your Android smartphone is based on Linux. A big, bad, scary computer operating system known only by people with neck beards. (Only, not really. But mostly.) Anyhoo, Android apps need permission to access certain parts of Linux, and not all apps have this special "root" access. That includes a few basic things, like the camera flash, and the ability to take screen shots. There are a bunch of other apps that need root access for other reasons, too, but the basic premise is the same.
So should you root your phone? First thing to do is read this editorial, and decide if you want to go further. Then if you're the type who loves to mess with things, go for it. If you want to squeeze a little more functionality out of your phone, go for it. Need more convincing? Check out "Rooting Q&A -- Is it for me?"