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Deadband is also known as hysteresis and is the amount of a measured variable (pressure, temperature, etc.) between the point where a switch closes and then re-opens. It can be implemented is software if you have an analog input (i.e., open at 1.02 PSI, close at 0.98 PSI) or designed into a switching mechanism. Often the deadband of a switch is fixed and cannot be adjusted. A typical example is in a wall thermostat in your house.
Most pressure switches use a diaphragm or bellow as the sensing element. The movement of this sensing element is used to. actuate one or more switch contacts to indicate an alarm or initiate a control action. Pressure switches have different designs with different sensing elements. One of the most common is the one with diaphragms or bellows as the sensing elements. The one I will discuss here uses a piston as the pressure sensing element. In any case, the operating principle for this piston type is the same with a diaphragm or bellow type pressure switch.