What can happen if there is air in the system and the pump does not make enough pressure to move it, is that the air expands as it heats up which pushes coolant to the reservoir and out of the overflow. That coolant is lost, so when the car cools down even more air is drawn into the system. You need to get rid of the air before the cycle of heating and cooling begins.
It is a problem that only affects a few models as it depends entirely on the design of the cooling system.
It's comparable to air in the central heating system of ones house. Air will collect in the tops of the radiators, particularly those on the upper floors, and sometimes can not be moved by the pump, hence the need to bleed the air at each radiator to restore flow.