Permissions let you control what users can do on your site. Each user role (defined on the user roles page) has its own set of permissions. For example, you could give users classified as "Administrators" permission to "administer nodes" but deny this power to ordinary, "authenticated" users. You can use permissions to reveal new features to privileged users (those with subscriptions, for example). Permissions also allow trusted users to share the administrative burden of running a busy site.
If you assign a permission to an anonymous user, the permission is not inherited by other roles. However, any permissions you assign to the Authenticated User role are inherited by other logged in users. For example, if you give the Anonymous role the permission to post comments, it does not mean that the Authenticated User role also gains permission to post comments. However, if you give the Authenticated User permission to post comments, it does mean that other roles you have created will automatically gain that permission.