core files are basically memory snapshots from when a program segfaults (segmentation fault, like walking past the end of an allocated array). If you aren't going to use them, delete them, as they don't serve any purpose other than to help debug why a program crashed. This is a one-liner to find all files named "core" on the system and delete them, though take care in doing so as not all files named "core" are necessarily core dumps:
find / -name core -type -f | xargs rm -f
Untested, but it should work (for every mounted filesystem)