We have a number of locked forums on our boards that a member might want to check but not keep open... Let me use myself as an example. I'm on the leadership team of our boards, so I have three different leadership forums unlocked (they are, of course, locked so only leadership can post/read there). We also have a number of other locked forums for various issues. I might want to check one of those locked forums if I need to, but then close it again so it's not always showing up in "View New Posts". Currently, to do that I have to log out completely, and then re-enter all of my leadership forum passwords. For the purposes of our forum, it's something that would come in very handy...
So basically, to answer your question, it boils down to posts from certain forums showing up in "View New Posts" and the member not wanting to see posts from that forum anymore.