Your backup will not work when this message is displayed!
Access to the backup output directory is restricted by your PHP open_basedir setting. This kind of restriction is applied by your host in the server's php.ini which is usually inaccessible to the hosting users (you). In short, open_basedir restricts the directories any PHP script can write files to. Setting the directory's permissions won't help; this is a system restriction imposed by PHP settings.
You must use another directory, residing inside the open_basedir allowed paths. Ask your host for more information.