Um, to be a little more specific

:
The name "core" comes from the old days when memory was made of ferrite cores. The term "core" was (and still is) used interchangeably with the term "memory".
When a program aborts abnormally, it tries to write the information it has stored in RAM to a file before it totally dies (this is called "dumping core"). The idea is that later examination of the contents of the file might help a debugger determine what caused the crash.
BTW- feel free to trash it, it's not doing anything but taking up space.