When transformer under full load, power transformer oil present in the transformer heats up and gets expand. During this process gas at the top of the oil gets expel out in to the conservator present at the top of the power transformer along with hot oil and cool oil from conservator comes down. This process is called breathing out of the transformer.
When the load on the power transformer is removed or during no load condition, transformer oil cools and air is drawn in to the transformer. This is called breathing in of the transformer. The incoming air may consists of moisture which should be removed else results in the deterioration of the dielectric strength of the transformer oil. Hence the air entering the power transformer is made to pass through the breather where moisture is removed from air through silica gel.