Jailbreaking is the process by which an iPhone firmware is modified to allow unsigned code to be run to gain access to files that Apple wouldn’t normally let you access. Jailbreaking adds unofficial application installers to your iPhone such as Cydia or Icy (I personally only use Cydia), which let you download many 3rd-party applications previously unavailable through the App Store.
The risks of jailbreaking your iPhone are very minor. Worst case scenario, you can always restore your iPhone to factory settings using iTunes.
