Here's a quick rundown of the way it works:
If a new post is made since you've last opened a board on the forum, the board is marked black to indicate something new has been posted, and each of the new posts has a little "new" next to it.
If you pop into a board, and there are new posts in 7 threads, they will all be marked with "new" next to them. Say you only have time to read 3 of them, 4 of them will still be marked with "new" next to them. If you leave the board or forum and come right back before another post happens, the board will not indicate a new post for you, because you already saw that there were those other new posts that you didn't have time to read.
It is designed to give you a two-fold level of indication for new posts: the "new" next to the thread remains there until you open the thread or click "mark read". This is a constant reminder of posts you have not read. The indicator from the main page of the forum only indicates new (turns black instead of grey) if there have been new posts in that board since your last visit.
I'm not sure how it handles posts made while you were reading another thread within a board.