You need to set files as favorite, to have access and see them on Dropbox when not connected to internet. Lean how to view Dropbox files offline on Android phones and tablets, by doing as follows:
1. Open "Settings"
2. Find the file you would like to use in offline mode
3. Tap the option icon
4. Hit "Favorite"
5. Wait to download the file completely
6. Now you can access this file from "Favorite" tab, offline
** To reverse the action and remove files from Favorite, tap "Favorite" icon again