A big core dump appeared in my home folder - what is it and how can I delete it?

Core files are essentially low-level crash dumps; by default, the shell doesn't allow them to be written (by setting a 0 byte limit on their size ulimit -c 0) because they're rarely useful for end users. You can see what the limit is currently set to by typing ulimit -c in the bash shell.

You should be able to get information about what program caused the dump using the file command, as described in this previous answer Find which program caused a core dump file or if you have the GNU debugger installed on your system, by running gdb -c core.

Unless you are interested in debugging the crash further, you can simply delete the file using rm core.

If you're not actively compiling / debugging executable programs you may want to set the core ulimit back to its default value to stop such files getting generated.