The Application extension gives you access to some additional application options that aren’t availble in the default AIR SDK.
The simple API allows you to quickly customise top level UI elements, such as status bars, in just a few lines of code. You can use the device information to identify a user, change UI based on operating system, determine device manufacturer and other device specific information. The user defaults can be used to save user settings in the native user databases, having all the advantages of using the native system for user settings.
This Wiki forms the best source of detailed documentation for the extension along with the asdocs.