Rarely does a developer have the luxury of building mobile apps for a single mobile platform. The fact is, the smartphone and tablet space is dominated by three big platforms: iOS, Android and Windows. Traditionally, this means using each platform's provided technology and SDK, i.e. Objective-C for iOS, Java for Android and .NET for Windows, or choosing a write-once/run-anywhere cross-platform toolkit which provides a lowest-common-denominator experience on all platforms, and prevents developers from going "to the metal" on any given platform to take advantage of the native features that make a mobile platform great.
With Xamarin, however, this limitation does not exist. Not only do you get a single, modern language (C#) and framework (.NET) across all three platforms, but you also get a native experience on each, giving your code direct access to the underlying SDK and device metal, including platform-specific UI and device capabilities, so that you can deliver a truly amazing native experience on every platform you target.