APNS - Apple Push Notification System
Try it and google for ready server solutions.
Update: Okay, lets get it longer -
APNS is the best way to inform user about something new. It works with every state of the app - even when app closed - and it helps to avoid unnecessary requests to server.
But you will need server to send pushes - if you can write it by yourself - it's nice, but the are some services to create backend for your app (no links - no ads, just google it).
To find out how to start with APNS on the client side and how to create all needed certificates and keys read this one
