The topics that have been posted to most recently will move to the top of the list. The most recent post in a topic will be at the bottom of the page. (I can reverse either or both of these orders, but this seems to be the most logical way to do it.)
If you are using the “default” theme for the forums (you have the choice of several), the folder next to the topic will be a darker color if it has new posts in it. Note you must be logged in to see the color difference as everything will be “new” if you are not logged in.
I too get no results with the “view new topics” function. But I’ve only tried it after I’ve read all the new threads. I think you have to have unread items for anything to show up.