Core
From Hackepedia
When a process receives certain signals it will exit and dump core. This is the state of the process when the signal arrived. A debugger such as gdb can be used to examine this corefile. A corefile can be called "core", "program.core" or even be configured to be written to a certain location (in FreeBSD).
The kernel also can dump core upon a panic or when instructed to do so. It saves the corefile to swap which is then transferred upon the next boot to /var/crash, it's a good idea to have the /var filesystem big enough to accomodate the size of the physical memory of the system.