DX10 will use much faster dynamic link libraries (DLLs), and won't incorporate older versions of DirectX, as is done today. DirectX 9 will be supported side-by-side, through DirectX 9.L (basically, that's DX9 for the Vista driver model). So right there, without using any new features, DX10 should be more efficient and faster.
The DX10 graphics API will usher in unified vertex and pixel shaders, and introduce the concept of "geometry shaders" that can act on not just single vertices, but whole triangles and their adjacent vertices. Developers will be able to stream out data from the GPU and reuse it without needing the CPU to do a single thing, so a lot of the CPU load seen in current graphics drivers and games should be reduced. DX10 should allow for more flexible and granular graphics memory access, and in general allow GPUs to be far more flexible and powerful than before.
Perhaps one of the best features of DX10 is the removal of capability bits, or "cap bits." Today, graphics cards don't have to support everything in DirectX 9 to be a "DX9 graphics card." There are lots of optional features, and the drivers have to report to the OS exactly what it can and can't do with a set of cap bits. This has been a huge headache for developers, as different cards all support different features, or perform the same operations in different ways. In DX10, either you meet the spec or you don't—no more supporting only these or those texture formats, and this or that shader model but only with this level of precision.