Aging in Transformers refers to the the reduction in the usable life over a period of time.
The main components of the Transformer are the windings, the core and the insulation. Of these, the windings and the core are made of metal. The windings are made of copper while the core is made of silicon steel. The aging in the metallic parts of the transformer is considered to be negligible. They are not subjected to the aging process. 
The aging of the transformer is thus considered to be related to the aging of the insulation. The insulation of most transformers is usually made of cellulose paper.
The factors which affect the aging of the insulation are
Air
Oxygen in the air causes degradation.
Moisture
Moisture or water content in transformer oil comes from two sources. The moisture in the atmosphere can be removed by the silica gel in the breather. Another source is the cellulose itself. As the cellulose breaks down due to aging, water is released into the oil. This water can be removed by periodically filtering the transformer oil.
Acids
Acids are formed, due to the degradation of the oil. The acids formed in the oil affect the insulation and reduce its life.
Heat
Heat causes the degradation of the oil. High temperatures also cause the insulation to break down. Hence, it is necessary to ensure that the transformer is operating within the temperature limits. The cooling system of the transformer should be properly functioning