XNA Framework is a yet another great thing by Microsoft. XNA Game Studio is a 3D interface for C# that runs on XNA & .NET Framework with Microsoft DirectX. Anyone can program 2D and 3D games in C# using Microsoft XNA Game Studio IDE and build games that provide best entertainment experience possible.
A game developed using XNA runs on Windows Vista, Windows XP and Microsoft's game console i.e. Xbox 360.
XNA brings all aspects of game production into a single system. The XNA toolset was announced back in March 2004, at the Game Developers Conference in San Jose, California; and a first Community Technology Preview of XNA Build was released on March 14, 2006. The final version was released on December 11, 2006.
 XNA Game Studio Professional is intended for professional developers who want to create commercial games for Xbox 360 and/or Windows. It is scheduled for release in 2007. XNA Game Studio Express is available with fewer options but enough to be familiar with the professional IDE. XNA Game Studio Express is actually for homebrews and developers that are not really professional but hobbyist.  
Word XNA is not acronymed. XNA is actually an airport code of US American Northwest Arkansas Regional Airport in Fayetteville/Springdale; Arkansas (check www.world-airport-codes.com) every airport in world is known by its unique airport code, like Airport code of Karachi-Pakistan is KHI. 

By: Umair Khan Jadoon (Co-writer - The Microsoft "Wow" Blog!)