This relates to a cards DirectX compliance. DirectX can be divided into two specifications, the Pixel Shader Model, and the Vertex Shader Model. Each model has different hardware requirements, and when you take both into account you can determine the overall DirectX version.
Think of this number as a more specific description of the DirectX version. Specifically, what pixel manipulation capabilities it has.
Does It Matter
Definitely. This number may directly affect the features that will be available to you in certain games.
Here's a brief description of the different versions:
PS2.0 - Came with the original DirectX 9.0 specification. First implemented in the Radeon 9700 Pro.
PS2.0a - Usually refers to the extended PS2.0 version supported by nVidia's GeForce FX line. Essentially a quarter of the way to full blown PS3.0. It supported far more instructions and features than the PS2.0 specification required.
PS2.0b - Refers to the shader model supported by the Radeon X700/X8*0 series. Could handle more instructions than PS2.0, but was still behind PS2.0a in instruction limits and features.
PS3.0 - Most notably added dynamic flow control making the gpu much more like a general processor (cpu). Also removed the ceiling on most instruction limits entirely and raised other limits significantly. This model is supported by all GeForce 6 Series and higher and all Radeon X1000 series and higher.
PS4.0 - Significantly raised nearly all instruction limits, added integer operations, tightened handling of floating point numbers, as well as tons of other features. This model is supported by all GeForce 8 Series and higher and all Radeon X2000 series and higher. This is generally considered to be a much more significant upgrade than was PS3.0.
For more details, check out the wikipedia article.