z is a complex number:
When drawn on the Argand diagram, z has the curious property that it can only have a magnitude of 1:
So z, which is the variable used in our frequency response, traces a circle of radius 1 on the Argand diagram. This is called the unit circle.
The map of values in the z plane is called the transfer function H(z).
The frequency response is the transfer function H(z) evaluated around the unit circle on the Argand diagram of z:
Note that in the sampled data z plane, frequency response maps onto a circle - which helps to visualise the effect of aliasing.