How do push notifications work from a networking point of view?
WiFi networks use "beacons" to allow clients to enter power-saving mode, but still be notified regularly if there is any traffic waiting to be sent to them.

Before entering power-saving mode, a WiFi device checks how often beacons are sent from the AP (typically, every 100ms, so ten per second, but some APs will let you vary it) and then wakes up in time to receive it. This beacon tells the client if there is any traffic waiting to be sent to it. Thus, it can still spend most of it's time powered down, but occasionally wake up to see if there's any real work to do. If there isn't, it immediately goes back to sleep again. And therein lies the powersavng.

Good page on it here: http://www.wi-fiplanet.com/tutorials/article.php/1492071/