When you are joining a new discourse install you get a bunch of “badges” for a variety of things, e.g. “First Like” or “First Quote”. Sometimes it’s also reply notifications that I have already read via mail.
I couldn’t care less about these notifications, but for some reason they will always remain as “unread” in the bar until I finally decide to click them because they annoy me so much.
So, the most general approach would be to allow clearing a single or all notifications’ unread status. I think it’s also debatable whether I have to read badge notifications in the first place.
Edit: Here’s a screenshot for better imagination: