How does Xamarin iOS and Android work?

I try to understand how Xamarin.iOS (MonoTouch) and Xamarin.Android (Mono for Android) work. I wrote a little App and looked into the .app and .apk file.

Inside of the .app file (iOS) are many .dll files. But why? On every page and post I read they say: The App is executed native and nothing is interpreted. Can somebody explain to me what the xamarin developer mean with "native"?

Inside of the .apk file is not a single .dll file..