Core files or Core dumps are actually snapshot images of the memory your PHP script used, at the moment of crash. This is produced as apache is compiled in the server with the debugging option. They are usually produced when one uses software packages that are not quite out of the beta testing stage or due to bug in the software packages.
There are many reasons for the core dumps. The most common being is that your PHP scripts are using a nonexistant function() or trying to use a disabled_function such as shell_exec, exec()
The core files are used by the developers for debugging an executable. finding out information such as, exactly where a program crashed, the values of various variables, the calling contexts, stack frames, etc, in order to ascertain the problems and to effect corrective measures prior to recompilation.
You could safely remove these files from your webspace, when they are created. Please be assured your account is not been hacked or access by anyone. Core files are system generated to enable debugging of PHP executables.
