What exactly does ‘authenticated’ mean for wp_ajax_nopriv?

Authenticated here means according to the is_user_logged_in() function, i.e. if the user is logged in or not, no matter the user role.

This part from the admin-ajax.php file, explains it all:

if ( is_user_logged_in() ) {
        /**
         * Fires authenticated AJAX actions for logged-in users.
         *
         * The dynamic portion of the hook name, `$_REQUEST['action']`,
         * refers to the name of the AJAX action callback being fired.
         *
         * @since 2.1.0
         */
    do_action( 'wp_ajax_' . $_REQUEST['action'] );
} else {
        /**
         * Fires non-authenticated AJAX actions for logged-out users.
         *
         * The dynamic portion of the hook name, `$_REQUEST['action']`,
         * refers to the name of the AJAX action callback being fired.
         *
         * @since 2.8.0
         */
    do_action( 'wp_ajax_nopriv_' . $_REQUEST['action'] );
}