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The option you are talking about is a label for posts by people who have not signed in to your web site.
For example, in the forum, if you post a reply your user name appears... however, someone who is not signed in writes a reply, instead of a user name it will say "Anonymous" or "Guest" or whatever you typed in as your label.
You can allow anonymous users access to any parts of your site you want to. This is handled in the Groups area (System Admin | Groups). If there is something you want anonymous users to be able to see, give the anonymous user group read access to that module or block.
Hope that helps.