I've found a more specific term than 'high-level' state to explain the router state is 'addressable state'. A single page web application has two types of state. Addressable state (which is stored in the Ember router) and then another form of state, let's call it non-addressable state which is stored in the controllers.
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).