This error message means that there is no archive(zip) utility installed for your site. This utility is used to make backups and also to zip up the log files that you will send to us.  We recommend that you  contact your hosting company. They will need to install a php zip utility for you to use WPBackItUp. 



Below is a link that you can forward to your hosts support.


http://php.net/manual/en/class.ziparchive.php