Flutter - How the NavigatorObserver class works?

// Register the RouteObserver as a navigation observer.
final RouteObserver<PageRoute> routeObserver = RouteObserver<PageRoute>();
void main() {
  runApp(MaterialApp(
    home: Container(),
    navigatorObservers: [routeObserver],
  ));
}

class RouteAwareWidget extends StatefulWidget {
  State<RouteAwareWidget> createState() => RouteAwareWidgetState();
}

// Implement RouteAware in a widget's state and subscribe it to the RouteObserver.
class RouteAwareWidgetState extends State<RouteAwareWidget> with RouteAware {

  @override
  void didChangeDependencies() {
    super.didChangeDependencies();
    routeObserver.subscribe(this, ModalRoute.of(context));
  }

  @override
  void dispose() {
    routeObserver.unsubscribe(this);
    super.dispose();
  }

  @override
  void didPush() {
    // Route was pushed onto navigator and is now topmost route.
  }

  @override
  void didPopNext() {
    // Covering route was popped off the navigator.
  }

  @override
  Widget build(BuildContext context) => Container();

}

This is a more detailed help guide. https://medium.com/flutter-community/how-to-track-screen-transitions-in-flutter-with-routeobserver-733984a90dea

Most of the time you don't need to implement NavigatorObserver. See this other StackOverflow answer explaining how to use push and pop to pass information between routes. In the use case you've described, you should addListener to an AnimationController, using the TickerProviderStateMixin to obtain a suitable vsync object. This ensures that your callback will not fire when the app is suspended or after your State is disposed. (Instead of addListener, you could use an AnimatedBuilder or AnimatedWidget the primary purpose of your callback is to rebuild a section of the widget tree.)

The main time when you'd want a NavigatorObserver is if you're using a plugin like Firebase Analytics. You can see an example usage in the plugins repo. You pass the NavigatorObserver in the navigatorObservers argument to the MaterialApp constructor:

static FirebaseAnalyticsObserver observer =
  new FirebaseAnalyticsObserver(analytics: analytics);
...
return new MaterialApp(
  navigatorObservers: <NavigatorObserver>[observer],
  ...
);

It is unusual to have a State that implements NavigatorObserver because your MaterialApp should be near the top of the widget hierarchy. At the time you're constructing it, most State objects won't exist yet so you'll have a hard time putting them into the navigatorObservers array. You might instead use a class that isn't a State. If necessary, you can use GlobalKey<MyClassState> to find the State that needs to be notified (but if you're doing this, there might be an easier way to accomplish what you want).