Brownouts are conditions where there is a sustained low voltage conditions. Low voltages affects the functioning of electric equipment. Lamps may glow dimmer, induction motors may draw more current to compensate for the drop in voltage and heat up. The loss of supply in one phase in three phase systems also falls under this category.
Blackouts are conditions in which there a loss of supply to a wide area lasting a few hours to many days. Blackouts are generally caused by a tripping in power stations or a malfunction in the distribution systems.
Dropouts have the shortest duration of all the three phenomena. Dropouts are condition where there is a dip in the voltage lasting a few cycles. It may manifest itself in the form of flickers in the lamps.