Windows Runtime or WinRT was officially introduced to the world together with Windows 8 in BUILD 2011. At that time, there were a lot of questions surrounding it such as, would it replace Win32, .NET, Silverlight, and so on? It’s almost two years, and I assume everyone has their own answers to those questions.
What is WinRT exactly? It is a new set of COM-based (i.e., every WinRT object implements IUnknown and does refcounting) native APIs on Windows 8. Every WinRT objects implements IInspectable which inherits from IUnknown. The API is defined in WinMD metadata format similar to .NET.
Windows Store App (formerly known as Metro-Style App)
The only type of applications that can be developed by WinRT are Windows Store apps. That’s why many people including me also use term WinRT app to refer to Windows Store app. However, there is no reason to think that, in the future, Microsoft won’t let developer to use WinRT to develop other kinds of app (e.g., desktop app). WinRT app can be run on both x86 (Windows 8) and ARM (Windows RT).
What does WinRT have to do with .NET?
WinRT app developed using .NET (XAML/C#/VB/F#) is still running on CLR which is the same CLR.dll that runs .NET 4.5 app. However, WinRT app is using a subset of APIs and is using different profiles (similar to .NET or console profile).
Silverlight/WPF/Windows Phone developers will feel at home when they are creating WinRT app although some APIs is missing (e.g., unrelated APIs like ASP.NET, COM wrappers) or moved to new classes (i.e., Reflection) or new namespaces. Like Silverlight, WinRT API is also asynchronous heavy (i.e., if an API can take longer than 50 ms to run, the API is asynchronous).
Here are some references if you want to learn more about WinRT:
WinRT demystified by Miguel de Icaza (Xamarin)
Underneath the Hood with .NET and the Windows Runtime by Shawn Farkas (MSDN Magazine)
Lap around the Windows Runtime by Martyn Lovell (BUILD 2011)
The Windows Runtime Q&A (BUILD 2012)
Rocky and Billy Introduce WinRT! by Rocky Lhotka and Billy Hollis (.NET Rocks)
Understanding WinRT and Windows 8 for .NET Programmers by Immo Landwerth (The Hanselminutes Podcast)
How does the new Windows 8 Runtime (WinRT) compare to Silverlight and WPF? (Stackoverflow answer by Pavel Minaev)
A bad picture is worth a thousand long discussions by Doug Seven
.NET and Metro: The Windows Runtime and the CLR on Windows 8 by Jeremy Likness