From the famous Wikipedia:
iOS jailbreaking is a process that allows devices running Apple's iOS (also known as iPhone OS prior to iOS 4.0) operating system (such as the iPad, iPhone, iPod Touch, and recently Apple TV) to gain full access (root access) to unlock all features of the said operating system, thereby removing limitations imposed by Apple. Once jailbroken, iOS users are able to download additional applications, extensions and themes that are unavailable through the official Apple App Store, via installers such as Cydia, one of a number of current means for older iPhones. 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 similar to rooting an Android device.
At its core, Jailbreaking a device gives you access to its root filesystem, allowing you to modify and install Third-party software component and modifications to that device. This allows you to be in more control of that device and allows many features that were previously unavailable without Jailbreaking that device.
Under the DMCA of 2010, jailbreaking is legal in the United States, although it voids Apple's device warranty. It is also legal in many other countries including those of the EU. The jailbreaking process, however, can be quickly and easily reversed by restoring the operating system through iTunes. Cydia creator Jay Freeman estimates that more than 10% of all iPhones are jailbroken.