Direct X is an API, that sets out standards for certain levels of Graphics generations, aswell as all multimedia support (keyboard,sound,mouse etc). This API allows game developers to design games under one "global" spec, so as to not have to design for each graphics card architecture.
In this spec, if we talk about graphics cards, we work with shaders as main identification of a certain DX level.
Shaders, pixel or vertex, are the means of how graphics are rendered on the screen. As the years fly past, newer shader instructions and code are used, which have to be supported by new graphics card in order to be compliant. This is hardware reliant, and hence you get DX8/9/10.
As an example:
DX8 had Pixel Shader version 1.0, and the later 8.1 had I think up to PS 1.3
DX9 had PS 2.0, and then DX9b had PS2.1b and DX9c had PS3.0
DX10 - this is a complete new API, and works completely different to the previous generation DX's due to unified architecture (dynamic load adjust to Pixel and/or Vertex shaders)
So, with each new DX, graphics cards need more "logic" to perform the added instruction. These "logics" refer to increased transistor count on the GPU. But, 5 years ago (very rough guess!) we had 150nm (the smallest wire connecting transistors on a GPU in nanometer) GPU chips, and this made it rather difficult to include a large number of transistors to the gpu, due to size, cost and heat constraints. This causes the growth in GPU power, and currently we are at a level where we can cram alot of transistors onto a GPU while costs, heat and size is managable. Currently, GPU's run on 110-80nm chips.
So, DX10 requires a new GPU, which right now can only be found on the 8800 or R500 in the Xbox (which isn't fully DX10, but hybrid between DX9 and DX10). Ati will release their DX10 card early in 2007, and I'd recon that the wait for it will be better, as price wars will then make the chips little cheaper.
As to the fact that you could install DX9, on DX8 chips previosuly, it boils down to backwards compatibality. Even if you run a DX8 card, you still use the latest DX9, as DX8 might be improved in new updates (for graphics). As already stated, DX does not only cover graphics, but input devices and sound aswell.
Now the sad part: DX9 can run in the Vista environment, but in a less supported (indirect) manner. So, certain VISTA features won't be able to run, aswell as the fact that DX9 games will be slowish in VISTA, aswell as running DX10 games in Vista using DX9 render path, resulting in the same scenario as before.
I'd recon, that VISTA will only be the sought after in Q2 of 2007 with regards to games in DX10. There is just too few, to warrant such an upgrade and the fact that your old DX9 games will be slow to begin with.
Don't get me wrong, I'm looking forward to DX10, but it will take time for this to establish itself...