what does the s-plane response of a system's transfer function describe?
This picture might help: -



Bottom left is an attempt at showing a 3D view of the pole zero diagram with the s-plane being flat to the floor so to speak. The example used is for a 2nd order low pass filter.

Note that the bode-plot (amplitude) and pole zero diagram are really parts of the same thing hence it's the complex frequency response that it covers.