The fridge acts as a heat pump. Thermal energy from the objects inside the fridge is transferred to a fluid and then transferred from the fluid onto the black grill. Now I'm not teaching I can say that it passes by conduction into the metal grill. From there, the thermal energy is transferred to the surroundings. This can be by conduction to air particles, which gives them more kinetic energy making them spread out. The result is lower density air that floats upwards. But there is also heat radiation, the emission of infra-red radiation. This is why the grill is painted black as this is the best emitter colour. The large surface area works well for both methods of heat transfer into the surroundings.