JailbreakMe is an app that jailbreaks (unlocks from a specific carrier) your iPhone. It allows full access to all functions built into the iPhone, as well as some apps that are not available through the App Store. JailbreakMe is itself not available through the App Store but is on many download sites including the authors' sites.
Before running JailbreakMe you should make a backup through iTunes so you can restore the iPhone to its original state should you have problems with JailbreakMe or any app installed once broken. Installing the app is as simple as running the download and then the phone is broken. You can configure your phone and apps using Cydia, then your phone has no ties to any provider or supplier. We tested JailbreakMe on both an iPhone 4 and a 4S and it worked cleanly on both.
JailbreakMe is probably the easiest and least expensive way to jailbreak your iPhone, but do make a backup before starting (and be ready to restore if you run into problems). JailbreakMe worked cleanly for us, and we were running apps only 5 minutes after starting the process.