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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 pump or water tank pressure control switch is designed and adjusted to turn the pump on at a cut in pressure, usually 20 psi or 30 psi, and to turn the water pump off at a cut out pressure, usually 40 psi or 50 psi.