A messaging service by Apple introduced with iOS 5. It uses the Apple Push Notification Service (APNS) to deliver messages that function equivalently to SMS and MMS messages traditionally carried over cellular networks. Instead of using the cell SMS delivery network, it instead travels over the data channel to iOS devices.
Functionally it also allows delivery and read receipts and is charged as part of network neutral data which in most parts of the world is substantially cheaper per byte than the SMS network charges. With the addition of an OS X client, the iMessage protocol will now extend the APNS service to both mobile and desktop/server OS running on Apple hardware.
Registration and addressing of iMessage uses the cellular number and/or iCloud (AppleID account) for authentication, authorization and access control to messages sent over the iMessage channel.
On iOS, iMessage is integrated into the Messages app, only kicking in when both parties are using an iOS 5 or 6 device. Apple feature page.
On OS X, iMessage is integrated into the Messages app that has different functionality than the iOS 5 Messages app. OS X Messages app also includes iChat functionality in its debut form running on Mountain Lion