How do iOS Push Notifications work?

Each device can be updated with data using their own unique device tokens. This picture explains everything . .

It was too much for me to put in a comment so.

From the documentation.

Apple Push Notification service (APNs) propagates push notifications to devices having applications registered to receive those notifications. Each device establishes an accredited and encrypted IP connection with the service and receives notifications over this persistent connection. Providers connect with APNs through a persistent and secure channel while monitoring incoming data intended for their client applications. When new data for an application arrives, the provider prepares and sends a notification through the channel to APNs, which pushes the notification to the target device..

I suggest reading the documentation for more information and how to use and configure. It's all there.

Push Notifications

I created an infographic to explain the workflow of push notifications. Hope this is helpful.

Device does not keep polling the server for the push notifications.

To keep it simple, consider an iPhone is connected to internet. On connecting to internet iPhone establishes connection to Apple Push Notifications server this connection is open connection which means data can be thrown to iPhone from server the moment data arrives to server.

Apple does not use HTTP protocol for Push notifications but if you understand HTTP Protocol its almost a similar methodology.

http://en.wikipedia.org/wiki/Push_technology#HTTP_server_push