What is "xamarin-forms"

The API Xamarin.Forms is used to quickly build native applications for iOS, Android e Windows completely in C#.

Xamarin.Forms is a library that allows you to create native interfaces for iOS, Android e Windows Phone from a single and shared source code in C#. It provides more than 40 cross-platform controls and layouts that are mapped to native controls at runtime, which means that their user interfaces are fully native.

Source:

https://developer.xamarin.com/guides/xamarin-forms/
https://www.xamarin.com/forms
http://www.hanselman.com/blog/XamarinFormsWriteOnceRunEverywhereANDBeNative.aspx