PubNub Android Sample
Code: https://github.com/pubnub/pubnub-api/...
This is a small sample app written in Java on the Android SDK. The video shows communication between two emulated Android Devices. You may imaging simple communication Apps such as Whatsapp. More complex apps such as Multiplayer Games are already in multiple Android App Stores.
Android Push Notifications:
https://github.com/pubnub/pubnub-api/...
Look into the BootReceiver.java file also the PushService.java and generally look into this folder for examples on how to get started with Android Push Notifications.