System notification message in message center
"NOTIFICATION SYSTEM" is not a system notification, or not one I've ever seen.  

The header is the 'app' generating the notification. In this case, as the icon looks like Safari then it could be some site you allowed to send you notifications.
(As I tend to have most of these switched off, I'm not certain if the wording they use in that header is Safari's or the remote site's responsibility.)

Safari > Preferences > Websites > Notifications



Check which sites you wish to allow to be able to do that - mostly you can switch them off, allow only the ones you really need, otherwise it's a spam-fest