You click edit. Then on the module of the right, go to the Categories and look for the one you want to get rid of. Click the trash can on the right end of it, and then save the page.
Interesting, it's one of those things you can't edit if you have source mode on default-- thanks for the heads up
It's not in the source code. But even categories you add in source can be removed in source; everything is stored in the module.
Another option, especially if you need to remove a large number of categories, is to edit using the monobook skin (can be done by adding ?action=edit&useskin=monobook
to the end of the url).
You can also disable the category module in your Preferences.
I previously used it, and complained loudly when it was needlessly disabled in source mode for a while, but I've had it disabled for a few months now.