The admin toolbar is only visible if there are visible links in it. The "Administration" link will only be visible to members of the Admins or Content Admins role, for a user in some other role that has page edit permission a link to PageTree.aspx will be shown and if the user has edit permissions on the current page then the "Edit this Page" and "Page Settings" links will be shown. If the user can create child pages below the current page then the "New Page" link will be shown.
See also Roles and Permissions and Creating an Admin Toolbar
Hope that helps,
Joe