Where to start...
AIR is a lot like Java in the sense that it requires a run-time engine to be installed. This engine has all "things" required to for the application to run. In a similar way, applications such as 3DMax or Word require that the operating system be present for them to run. Those programs are written using API calls that are present within the target operating system. Likewise, AIR and Java apps are written using API calls that are present within their run-time. To bring it full circle, AIR is an application written in C, that uses APIs for the target operating system. So, when you perform certain functions within AIR, it then knows how to execute needed operating system functions (as needed). AIR also provides a lot of higher level functionality and management that make your life as a programmer a lot simpler.
Looking at iOS or Android, we have the same thing happening. Some developers are writing apps using Objective-C (iOS) or Java (Android) that are using APIs specific to those operating systems. This is the same as writing your app in C like 3DMax.