You will not be notified of anything about new topics in these categories, and they will not appear on the categories or latest pages.
So far, this feature doesn’t work for me. (*)
I have not tried to log in and out yet. But revisiting the Profile menu shows that it remembers which categories I’d like to mute. It just didn’t seem to take effect (yet).
(*) It hides the muted ones in Categories view, but it still displays posts from those muted categories in Latest. Maybe it only applies to new posts going forward, time will tell.