If you go to the specific forums, they will be ordered by last post. The bold threads at the top of the list [below the sticky threads] with the little downward arrow on the left are the ones that have had posts since the last time you logged in.
Likewise on the main forum list, if the flag to the left of the forum is a red dive flag, it means that forum has new posts since you've last logged in. If the flag on the left is a blue alpha flag, then there aren't new posts.
So you can do exactly what you wish by going into each forum, now they are grouped by forum. The 'New Posts' feature [basically] just collects all those threads and sorts them together by date.