Difference between four matrices of state space?
All four of the matrices interact with the system at different points. I think the best way to understand them is to look at the formulae while referring to the general diagram:


Figure 1: "Vector block diagram for a linear system [...]"

When you look at the above diagram we can see that the four matrices are in various points that correlate with their general names. \$B\$ is at the input, \$C\$ is at the output, \$D\$ feeds the input forward to the output (feed-forward), and \$A\$ is in the heart of the system mixing with the integrator.

The input signal \$u\$ is fed through the input matric \$B\$. Following that conversion, it is added to the signal \$x\$ passing through the system matrix \$A\$:

$$ \dot{x} = Ax + Bu$$

The input \$u\$ is also "fed-forward", by-passing the system, through matrix \$D\$ and it is added together with the output of the inner system \$x\$ multiplied by our output matrix \$C\$:

$$ y = Cx + Du $$

This is the general diagram. The values of the actual matrices change how the block diagram would look. For example, if \$D = 0 \$ there would be no feed-forward portion on the upper part of the diagram.