Suffocation via a plastic bag is caused by a process called asphyxia. Asphyxia occurs when the airway becomes obstructed, causing oxygen deprivation in the body.
As plastic bags are generally made of non-porous materials, a bag placed over the head effectively cuts off the oxygen supply. When this happens, oxygen levels in the blood quickly drop below sustainable levels, the person loses consciousness, and death usually follows within just a few minutes. Plastic bags are not the only cause of asphyxiation, however. Any airtight environment can produce the same results, as can environments in which oxygen is replaced with other gases.