Just what it says. Posts that you have not read.
When you click on it, you see THREADS that you have seen before. The fact that a thread is in the list indicates that there are unread posts within those threads (i.e. additions to the thread since you last opened it).
What exactly does "New Unread Posts" in the FORUMS tab mean?
After clicking on it, I see a lot of posts that I have seen before - even commented on, let alone read. There are quite a few with over 100 comments.
What exactly is "New Unread Posts" supposed to mean? And how is it different from "Unanswered Posts"?