Xamarin has "ported" a subset of the .NET framework to work with Android, iOS and OSX. Recently, Microsoft has made available a new profile (Portable Class Library project) that ensures cross-platform compatibility across Xamarin (Android and iOS) and Windows Phone.
By "porting", I mean Xamarin exposes the Android and iOS APIs via C# bindings, allowing you to build apps using C#, and more easily share non-UI code across the different mobile platforms. Xamarin Forms is an extension that makes it easier to share UI code across these platforms. However, Xamarin Forms is best suited for simple apps.
See this link for more info:
How does Xamarin work?[
^]
/ravi