DX11 adds some new features and one of them is Direct Compute, which uses GPGPU technology, which basically uses your gaming card for processing instead of just your processor, thereby giving you extra performance. This can also be used in games for physics.
Anyway, unlike DirectX 10 (Unified Shader Model 4), which was found in Vista and required either AMD's ATI Radeon HD2000/3000/4000 series, or NVIDIA GeForce 8/9/200 series of DX10 gaming cards, DX11 can function on DX10 gaming cards as well, albeit not as fully as on DX11 gaming cards, which is the ATI Radeon HD5000 series, or NVIDIA GeForce 300 series (which isn't out yet).
As expected, this means DX11 can also work on Vista, and it can, when Microsoft releases the Vista Platform Update, but like the above DX11 and DX10 compatibility, you won't get the full features as compared to a pure DX11 platform, which is Windows 7 with DX11 gaming card, and in this case, only ATI's HD5000 is out.
This is where XFX comes in. They have released their XFX Radeon HD5800 series of gaming cards - which is the XFX Radeon HD5870 and the XFX Radeon HD5850 gaming cards. With this, coupled with Windows 7, you'll get the full DX11 deal. To sweeten the deal even further, there's a Dirt 2 game bundle, and yes, Dirt 2 is DX11 to get the game ball rolling. See here for a list of other upcoming DX11 games.
Of course, with DX11 you can also play DX10 games, and you can see a list of DX10 games here - but remember to update your DX files! If you haven't done so, you can get it for free from Microsoft's site here (100MB). Even if you're using Windows XP with DirectX 9, it will update your files to the latest DX9. This might help if you're having problems running some games.