What is that core file that keeps popping up in various places. Can I get rid of it or what?

A core dump is an image of the memory held by a program when it crashed (or manually generated in some cases). It is used with debuggers (like gdb or dbx) to figure out what exactly got wrong. (Or in the case of a voluntary core, to restart the process later).

Yes, you can get rid of all your cores if you don''t care for debugging.

You can set ulimit -Sc 0 to prevent coredumping completely. Some distros do this by default
(the S means Soft limit, i.e. you can raise the limit later if you need coredumps for debugging).

cu,
Prefect