Jailbreak - To gain access to the iPhone's private file system, hence gaining the ability to override some of the iPhone's restrictions. The use of jailbreaking an iPhone is to gain the ability to install third party applications.
Jailbroken Apps - Third party applications which run only on iPhones that have been jailbroken (aka have had their private file system opened). These applications are not approved by Apple. Jailbroken apps can be downloaded from various repositories using Installer or Cydia.