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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.
A pressure switch does this by applying the process pressure to a diaphragm or piston to generate a force which is compared to that of a pre-compressed range spring. A pressure switch is used to detect the presence of fluid pressure.