DirectX 11 adds new stages to the graphics pipeline. These new stages are called the Hull Shader, the Tessellator, and the Domain Shader.
The Hull Shader and Domain Shader basically operate in support of the Tessellator. The Tessellator itself is a way of increasing scalability of game characters, as it aids in chopping up a character being rendered into smaller pieces which can be rendered or not rendered, depending on the level of detail needed. The use of character models that scale in terms of detail depending on how they close are to the player and the graphics hardware the game is running on has been a popular topic for years now, but the potential of scaling character models is far from exhausted. The inclusion of a tessellator in the graphics pipeline of DirectX 11 will give developers more tools for scaling their character models, and this should in turn make DirectX 11 games more capable of presenting acceptable graphics when used on low-end hardware while at the same time presenting appealing graphics when used on high-end hardware.
Also added by DirectX 11 is the compute shader. There has been much talk recently about using the large amount of computing power available in graphics hardware for tasks other than rendering graphics, and the compute shader is aimed to help developers harness that compute power for non-graphical tasks, a job that is currently supported by both Nvidia and ATI, but using their own proprietary systems. DirectX 11 should make standardization possible, which in turn should make the use of video card compute power for non-graphics tasks more common. If developers know that they can use DirectX 11 to harness GPU compute power, and that this will work on any DirectX11 compatible hardware, they will be much more inclined to use GPU compute power of their own volition, rather than because ATI or Nvidia is pushing some extra cash or marketing deals their way.