What is Jailbreaking of iPhone / iPod

Jailbreaking is a process that allows iPad, iPhone, iPod Touch, and recently Apple TV users to gain root access to the command line of the iOS operating system, thereby removing usage and access limitations imposed by Apple. Once jailbroken,[1] iOS users are able to download extensions and themes that are unavailable through the App Store (via installers such as Cydia) and perform other tasks that are not possible on store-bought devices, including installing non-Apple operating systems such as Linux. A jailbroken iPad, iPhone or iPod Touch running iOS can still use the App Store and iTunes and other normal functions, such as making telephone calls.

Jailbreaking is different from SIM unlocking, which, once completed, means that the mobile phone will accept any SIM without restriction on, for example, the country or network operator of the owners choice. Under the DMCA of 2010, jailbreaking is legal in the United States, although Apple may claim it to void your warranty. It is also legal in many other countries including the EU. The jailbreaking process can be quickly and easily reversed by restoring the device in iTunes.

Cydia creator Jay Freeman estimates that over 10% of all iPhones are jailbroken.

Some more definitions and analysis:

In essence, jailbreaking your iPhone means freeing it from the limitations imposed on it by AT&T and Apple. You install a software application on your computer, and then transfer it to your iPhone, where it "breaks open" the iPhone’s file system to allow you to modify it.

Why Would I Want to Jailbreak My Phone?
It lets you do everything from customizing the look of your iPhone to installing third-party applications and customized ringtones on it. Depending on how far you're willing to go, you can do even more than that: Jailbreaking even lets you to unlock your phone so you can use it with a carrier other than AT&T.

Why Wouldn't I Want to Jailbreak My iPhone?
Once you do it, you're on your own. You may have voided your warranty, so you can't rely on AT&T or Apple to fix any problems you encounter. All of the applications that jailbreak your phone are unauthorized and could damage or completely disable your iPhone. Your slick smartphone could end up as nothing more than a very expensive paperweight.

Can I Fix My iPhone if Something Goes Wrong?
Maybe. Some users have reported that they were able to connect a malfunctioning iPhone to iTunes and restore it to its original settings, which resolved the problem. Not all users have had this experience, though, and you certainly can't count on AT&T or Apple to provide you with tech support once you've taken this unauthorized step.