Coredumps are used for analysis and debugging if/when a ESX host "crashes" with a "kernel panic". This is visualized by a purple screen (often called PSOD, similar to Windows'es "Blue Screen Of Death").
VMWare ESX 5.5 and newer introduces the ability to perform coredumps to a file instead of a partition.
To configure this, you need access to the ESX host's CLI (either through vSphere Management Assistant (vMA), directly on the host through console or SSH, or some other method). For this to work, you need "root" access (or the equivalent of it through vMA).
ls -l /vmfs/volumes
esxcli system coredump file add -d DATASTORE_UUID -f FILENAME
esxcli system coredump file list
esxcli system coredump file set -p /vmfs/volumes/DATASTORE_UUID/vmkdump/FILENAME
To remove a coredump file, you can use a similar command to remove it:
esxcli system coredump file remove -f /vmfs/volumes/DATASTORE_UUID/vmkdump/FILENAME
Note that to remove a specific file, you need to do this on the host that is actively using the dumpfile, or else you will get a "Device/resource busy" error message. Also, if the file is actively in use, you may need to specify --force to forcefully remove the file (which will actually deactivate it before removing it).