At first, I thought this was most likely an instance of Android cloud to device messaging, but it can't be: WhatsApp doesn't declare the necessary permissions, and it works in Eclair (Android 2.1), while cloud to device messaging (and its replacement, Google Cloud Messaging) require at least Froyo (Android 2.2).
However, it is most likely some sort of push notification service. It's impossible to say exactly how it's implemented without access to WhatsApp's source code.
The part about it being able to receive messages when not in use is relatively easy to explain, though. The app almost certainly has a service which runs in the background to check in with the server periodically (or receive the server push, or whatever it does). When you receive a message, the service pops up a notification.
As for the question as to how the server could do a push, here's a possibility (again, I can't verify without source code):
- WhatsApp starts and opens two sockets: One to listen on and one to send a message to the server.
- WhatsApps starts listening on the first socket.
- WhatsApp sends a message containing your phone number and the port of the listening socket to the server and waits for an acknowledgement.
- The server records the phone and port numbers in the message and the IP address that the message came from.
- The server sends an acknowledgement to the app.
- The app receives the acknowledgement and closes the message socket.
- A message with your phone number as the destination comes into the server.
- The server uses the IP address and port number it has associated with your phone number and uses that information to push the message to your phone.
For this to work, the app would need to monitor the state of the network connection and reset the listening socket / resend the registration message when necessary (if the IP address changes, for example).