Suffocation or asphyxia is a cause of respiratory arrest, which is resulted by the inability of air to reach the lungs, almost always, due to some sort of physical blockage. It's the mechanism, which causes death in many diseases, such as anaphylactic shock or traumatic injury to the trachea.
When air cannot reach the lungs, carbon dioxide builds up in the lungs and, eventually, there is not enough oxygen supplied through blood the pulmonary vein to drive the heart. Shortly after respiratory arrest, the result is a heart attack from lack of oxygen in the coronary artery and cardiac arrest.
In an emergency, medical personnel must remove the blockage or bypass the blocked area. Typically, this results in a tracheotomy, as in most cases, any swelling that might be blocking the airways is above this point.