Thanks guys.
The particular Applet Windows I'm talking about are all a part of the page building process. Important things happen in these windows. For instance, one of them is the window I'm in while I'm building a page. Another is the window I'm using when I access my hard drive or a floppy in order to upload pictures to my site.
So I think Mudguard has probably answered at least part of my question when he said that Applets can access my system. And maybe that's why they come with a warning.