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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, or water level control, allows your washing machine to detect when it's sufficiently filled. It can then close the valve from which your home or building's water pressure pumps water into the machine. Your washer contains an air-tight hose that runs from the body of the washer to the pressure switch.