Hi Nicholas,
files are downloaded to your device for offline access:
- Android: /sdcard/Android/com.moodle.moodlemobile directory
- iOs: Inside the application sandbox, I think that you can browse the files if you use Xcode or itunes, but I'm not sure. As far as I know, It's complicated browse that files, see here for more info: http://apple.stackexchange.com/questions/54682/easiest-way-to-browse-iphone-filesystem