It is an element of a feedback-loop and therefore evaluated by application of control theory.
It has two setpoints on which it switches abruptly usually involving a hysteresis.
It may be used in a heating and cooling situation or for two speed control.
The "double-bang-bang" was implemented in the Luft Instruments Model 77 Controller used in a variety of laboratory (titrations) and plant application.
Shown in Harvard University Science Museum.