In commit 36da4cd (followed by 2 minor tweaks later) we added the ability to share content from your app with other apps on your iOS/Android device. On iOS this means that you can for instance share files with your Mac using AirDrop, send an email with files attached, share to DropBox etc. On Android this means that you can for instance send files to Google Drive, send an email, share to Hangouts etc. The number of supported targets depends on installed extensions/apps.
On both OSes you can send text, internal files your app creates (e.g. in a temporary directory), files embedded in your app bundle, images and arbitrary data. For Android, remember to enable Content Sharing in Projucer first:
Let us know if you encounter any issues with sharing, especially on Android where there is no one consistent way each sharing target behaves. JUCE Dialogs Demo has been updated to include the new sharing options.