A crash reporter is a software application whose function is to identify report crash details and to alert when there are crashes, in production or on development / testing environments. Crash reports often include data such as stack traces, type of crash, trends and version of software.
Crashes are unexpected shut downs of Minecraft. When Minecraft crashes, it typically closes immediately, though it may show an error report marking the location of the exception which caused the crash. A sign of a crash is a "Saving chunks" or "Shutting down internal server" screen.