This refers to the change in some electrical parameter of a device with induced stress. Like how a microphone works, but it need not be sound that induces the stress.
Microphonics refers to the manifestation of stresses on components and assembles translating into a change in the operation of the devices and subsequently appearing as a spurious signal in the circuitry. The mechanisms are varied, the devices may be piezo-electric but there are other mechanisms. A microphone picks up subtle pressure variations in the air and turns them into an electric signal that is an analog to the sound waves; here it may be a board flexing, a component being stressed. Often these microphonic induced signals will look/sound like audio signals - thus the parallels to a microphone is appropriate.