-CHEAD (which I would generally spell as -C HEAD instead) is unnecessary here, but its meaning is simple enough. As the git commit documentation notes, the -C option is short for --reuse-message:
-C <commit>
--reuse-message=<commit>
Take an existing commit object, and reuse the log message and the authorship information (including the timestamp) when creating the commit.
This is similar to the -c (lowercase) option, with one simple difference:
-c <commit>
--reedit-message=<commit>
Like -C, but with -c the editor is invoked, so that the user can further edit the commit message.
So -C commit is equivalent to -c commit --no-edit, or, if you prefer, swap the case of the c option and add --edit.
The name HEAD, in all uppercase, works as described in the gitrevisions documentation:
HEAD names the commit on which you based the changes in the working tree
(or equivalently, the currently-checked-out commit). So -C HEAD means to take the commit message from the current commit, without editing it.
With --amend, --no-edit means to take the commit message from the current commit, without editing it, and --edit means to take the commit message from the current commit, but stop to edit it. So this is exactly equivalent for --amend. For other commit options, the -C, -F, or -m option specifies the source of the initial commit message that may either be edited or not-edited as specified.