The Public Homepage option, when checked, tells the plugin to allow anonymous access to your WordPress front page.
Obviously, this option is only available when you previously activated the Intranet authentication scenario. You will find that the Public Homepage option is not visible when you activated the Internet authentication scenario, because in this case the plugin will already skip authentication for any published WordPress page or post (and this includes the website’s homepage).
Simply check the option to make the front page of your WordPress available to anyone i.e. to grant anonymous access to the homepage of your WordPress website.