The inbox on the communities serves much the same purpose as the notification center on your smartphone - an overview of all your alerts, and allowing you to act on them. The inbox on the communities, however, lets you see all alerts, or only unread. To change your view simply follow below.
1) Go to your inbox
2) All notifications you've received will appear by default, but select Unread Only - and only unread will.
You can always switch this option at anytime, and none of your previous alerts will be deleted.