Some months ago, Google looked to be rolling out a new interface for notifications in the Google+ app. No sooner did we report on it than Google removed the new notifications with a server-side switch. Google giveth, and Google taketh away. Today, Google giveth. The new G+ notifications appear to be rolling out for real.
So, what will you see in the new Google+ notifications? Only what you want, which is rather the point. There are now filters accessible at the top that allow you to see only unread notifications, all notifications, or other updates (things like new followers and collection updates). This should make it easier to triage all those G+ notifications you're getting.
The other tweak has to do with dismissing unread notifications. When Google originally went to the new notification screen, you could only dismiss notifications by swiping right to left. Now you can swipe either way.
It's possible you've had these features for a while—some people seem to have been on the new version for months. For the rest of us, it seems to have switched over very recently. You should see the changes if you go to your G+ notifications right now, no app update needed.