A make-up air system is an HVAC solution that adds fresh air back into a space that was once removed. The fresh air that is pulled in replaces the existing air that is not recirculated. Most make-up air systems are used for buildings that need more ventilation to ventilate the air and protect the people inside the building.
Whether an air conditioning system needs make up air depends on the system. If the HVAC system exhausts air outdoors, then you will need make up air. This is so you can replace the air that was lost. However, if you are using an HVAC system that does recirculate the air, then you will not need a make-up air system.