It bypasses apple security and installs a program called cydia. From there you can download apps that are not approved by apple and thus do things not possible without a jailbreak.
It had some more key uses on the iPhone, but on the iPad it allows things like much greater customization of the user interface, running iPhone apps in retina resolution rather than 2x, tethering stuff, emulators, quick access menus and dozens of other things. People also use it to pirate official apps but obviously that's illegal, where as the rest is not.
Search "top Cydia apps" in google if you want to see some of the things available. Of course, as you can see we are still waiting for the iPad 2 jailbreak.