What is meant when it is said a CCD's response is nonlinear? Does it mean the value of a pixel of the camera is not proportional to the number of received photons? Does it involve saturation? What factor expresses this?
Yes, non-linear simply means the signal out isn't proportional to the light received.
CCDs are inherently very linear (until they saturate) but the readout electronics might not be, especially if the camera system isn't designed for precise scientific measurements.
Systems for TV are deliberately non-linear (see gamma correction) to allow them to show a bigger range of scenes in the limited dynamic range of a TV signal