An example Android app using MQTT protocol
MQTT is a publish-subscribe-based messaging protocol, this means that clients must subscribe to a specific topic where messages are sent. The MQTT broker (or server) is in charge of managing of sending message to a specific (or specifics) topics and all clients subscribed to it will be receiving the data.
The implementation of this protocol was developed thanks to Eclipse Paho project. You can check an article I wrote for The Android Pub about this project here: About the MQTT protocol for IoT on Android