Rooting an Android phone is similar to "jailbreaking" an iPhone. If your Android phone is "rooted" you can access and modify Android's root files. These are the files inside its system which is basically hidden. Rooting is used in many ways such as customizing the Android phone's framework/theme, changing boot images, and more.
How to root?
You can use apps dedicated to root an android phone such as Universal AndRoot, and Z4Root. These apps are found in the Android Market. You can also Google them.
Disadvantages? You'll just loose warranty if they find that the phone rooted. XD