When the New Posts button in the navigation bar is clicked you will be presented with a list of all posts in reverse-chronological order.
Additionally, threads with posts made since your last visit will be flagged with a new icon to the left of the thread subject title. If you click on this icon you will be taken to the first new post made since your most recent visit.
If you click the "new" icon to read new posts, then click the New Posts navigation button again, you will see that the thread you just read is no longer flagged as new.
Also, when you click the Participated button (top, right-side) you will be presented with a list of the threads that you have participated in.
If any of those threads have new posts since your last visit, the Participated button will have a new icon in front of it.