Is there a document somewhere that describes what the Mobile app can achieve offline? I'm guessing that it can only provide the content for review, and possibly some simple user input for later sync. But it would be good to know for sure.
Essentially, pages and related files that you view while online will be cached so that they can be viewed again when offline. If you press the download icon for a resource or activity, they will be pre-cached so that the app will behave as though you had already viewed them while online.
Here are some relevant documentation about offline features: https://docs.moodle.org/35/en/Creating_mobile-friendly_courses#Offline_activities, https://docs.moodle.org/35/en/Moodle_app_features, Moodle Mobile offline features - Presentation in the MoodleMoot UK 2016 (https://www.slideshare.net/juanleyva/moodle-mobile-offline-features), and https://docs.moodle.org/35/en/Moodle_app_synchronization