A valve with deadband acts like there is some backlash between the controller output and the actual valve position.
Every time the controller output changes direction, the dead band has to be traversed before the valve physically starts moving.
Although dead band may be caused by mechanical backlash (looseness or play in mechanical linkages); it can also be caused by excessive friction in the valve, an undersized actuator, or a defective positioner.
Many people use the term Hysteresis instead of dead band but the ISA clearly calls the mechanical backlash phenomenon in control valves as dead band.