The XNA Framework Redistributable download provides game developers with the XNA Framework run-time libraries they can include with their product for redistribution on the Windows platform.
Microsoft XNA Game Studio 4.0

Microsoft XNA Game Studio 4.0 makes it easier than ever to create great video games for Windows-based PCs, Xbox 360 consoles, and Windows Phone.
XNA Game Studio 4.0 is a programming environment that allows you to use Visual Studio 2010 to create games for Windows Phone, the Xbox 360 console, and Windows-based computers. XNA Game Studio 4.0 includes the XNA Framework 4.0, which is a set of managed libraries designed for game development based on Microsoft .NET Framework 4.