An app developed by xamarin has the mono runtime which it takes with it onto the device. The app apk contains .net intermediate code, p-code, which obviously is not Dalvik understandable.
Xamarin.Android developers access the various features in the operating system either by calling into .NET APIs that they know (for low-level access) or using the classes exposed in the Android namespaces which provides a bridge to the Java APIs that are exposed by Dalvik.
http://docs.xamarin.com/guides/android/under_the_hood/architecture/ this is where you can find more details.