Xamarin creates mobile app development tools that are built on top of the Mono Project. Xamarin always provided, arguably, the most polished cross-platform development environment, but, it was pretty pricey. Recently Microsoft acquired Xamarin, and in the new spirit of openness Microsoft has made Xamarin free. That means it costs nothing to developers and you can also look at the code and even contribute if you're so inclined.
There are some services that you still need to pay for such as Xamarin test cloud and training in Xamarin university. But, those are extras most developers and organizations can do without. The organizations that do require them usually can afford to pay for them.
Why is it such a big deal? Xamarin provides a mature, well-thought-out and well-engineered solution for cross-platform app development.
With Xamarin, you develop in C# and have the power of the .NET framework behind you. Xamarin does the heavy lifting of translating your C# code to the native mobile OS. You can target iOS, Android and, of course, Windows phone. Xamarin provides an interesting mix of approaches. You get cross-platform capability with Xamarin.Forms, which gives you the native look and feel and you can also get full access to each target platform capabilities using Xamarin.Mac and Xamarin.Android. The main benefit is that you can start prototyping, and even begin actual development quickly, for all supported platforms using Xamarin.Forms, knowing that if you do need to write low-level platform-specific code this route is always open to you and it will integrate cleanly with the cross-platform code.