"Application state", rather than "stateful vs stateless" state. The router specifies "I'm looking at a post now" and the controller specifies "Looking at a post means loading this particular Post model as well as these comment models"
As an example you could have a web application that has multiple documents and inside each document there are panels that can be expanded and collapsed. As you switch between documents each document maintains its own version of which panels are expanded or collapsed.
In the Ember world the router would maintain which document was opened (addressable state) and the DocumentController would maintain which panels are opened (non-addressable state).