I think it shows any conversation where you did not make the last reply. That's probably why I have 8 Conversations still showing - those are the ones where the other person made the last response. This means that in order to close out a conversation, I am forced to make the last reply. Then to close it out on their end, they have to reply to me. Which re-opens it for me, forcing me to reply...
I think you can see the problem, no? It means we're going to end up in infinite loops, at least if people are as OCD as I am. This is wasteful of time, and forum resources.
If there were a way we could mark a conversation as finished, it would be better. That way we'll be more likely to notice if we have a new PM, because the number will otherwise be blank.
Or, if the Notifications bothered to mention PMs, instead of notifying us when someone quotes a post we make on the forums. I don't know why the forum feels it is necessary to give me a Notification for that. It might be useful if this forum were busier, but as it is, I check every thread that gets a new post, and right now I have to manually delete the notifications, since they don't clear when I visit those threads. If they notified us of PMs, that would be a far more useful function. If there's a way to set it this way, that would be nice.