A damper is an HVAC component in a ducted system, that controls how much air (cold or hot) goes into each space via ducts (metal pipes/corridors normally located in the ceiling).
Ducted air conditioning systems may also be known as 'central air' because the outdoor unit does all the work to condition the air to the right temperature, and then this air is sent to different rooms or spaces through ductwork (metal pipes/corridors normally located in the ceiling).
A damper is an HVAC component that takes care of controlling the airflow in the ductwork and therefore helps to adjust the room temperature by deciding the amount of air that is sent to the different zones of the duct system. Similarly dampers, as part of a zoning kit, can be used to control airflow in a non-ducted system in cases where one indoor unit needs to serve 2 or more distinct areas with slight variations in temperature and/or airflow.
Dampers can be controlled automatically or manually. Levers located outside of air vents and ducts control damper plates or valves in a manual system. The automatic ones work mechanically and can be managed remotely.