I gave a Lunch and Learn about Xamarin at the Logical Advantage office on September 20th, 2016. I contributed to "everything you need to know about Xamarin", a Q&A article about my event, which was posted to the Logical Advantage blog leading up to the event.
Xamarin is a framework to develop a cross platform mobile application using C#. Developers have many choices for building mobile applications. There are many frameworks and platforms to pick from like Ionic, Swift, Objective-C, and Java for Android. Xamarin was really strong, but now its gaining more momentum since Microsoft has purchased them ($400M) and is offering as part of Visual Studio and MSDN subscriptions. You may wonder what the benefit of Xamarin is compared to other cross-platform tools. Most cross platform tools use web technologies which do not look like native apps and incur significant performance costs compared to coding in the platform's native language. The C# code that you write in Xamarin will perform as good or sometimes better than code that you would write in the native languages.
Here is the slide deck from my presentation for anyone who missed it. This presentation was largely borrowed from the Introduction to Xamarin slide deck, thanks to James Montemagno.