Technical Definition of Jailbreak:

The iPhone and iPod touch 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 or iPod Touch that users aren’t supposed to mess with. Typically, this is an immediate prelude to either installing cool programs, unlocking the handset for use with another cellular network, or both.
Through jailbreaking, you are able to add additional applications to your iPhone or iPod Touch. It allows you to do so by adding an application called Cydia to your iPhone or iPod Touch. It also allows modding (changing) of your iPhone/iPod Touch application icons, wallpaper, dock, status bar, chat bubbles, weather backgrounds, keyboard….etc.

  Source: Apple iPhone School

==========================================================
More Info From Wikipedia...