When a program crashed the contents of its memory may be written to a file. This information can then be used to determine why the crash happened.
This can happen with both regular programs as well as well when the OS panic. Such a file contains the core memory and hence it as called a core dump. Other names used for it as system dump and memory dump.
Dump can also be triggered on demand. E.g. with
kill -SIGQUIT process_id.
man 3 abort.