What is jailbreak? What does jailbreaking means?

Technical definition of Jailbreak:

The iPhone, iPod Touch & iPad hack that allow users to gain access to the entire UNIX filesystem. In UNIX terms, this refers to changing the root of the directory tree to /.

Understandable definition of Jailbreak:

A hack that gains access to areas of the iPhone, iPod Touch or iPad that users aren’t supposed to mess with. Typically, this is an immediate prelude to either installing cool programs (usually applications rejected on the official AppStore), unlocking the handset for use with another cellular network (unlock), or both.

Through jailbreaking, you are able to add additional applications to your iDevice. It allows you to do so by adding an application called Cydia or Rock to your iDevice. It also allows modding (changing) of your iDevice application icons, wallpaper, dock, status bar, chat bubbles, weather backgrounds, keyboard, etc.

Disclaimer: Jailbreaking voids your warranty.