Asphyxiating or suffocating in your dream generally bears a negative significance referring to eventual health disorders or misfortune in your waking life. If you feel that you run out of air in your dream, this may be a metaphor for feeling overwhelmed or overcome by a situation in reality. The dream may also stand for a relationship of any kind in which you are smothered and controlled, therefore literally suffocated by your partner(s). It may be the relationship with your lover, with a member of family or a close friend which has limited your freedom and has turned you into a victim.
If in your dream you are the one who suffocates other individual, the interpretation is reversed - you may be the 'tyrant' who wants to control and oppress people you have relationships with. Or you may desperately want to break free from a situation/relationship which has kept you captive for too long. There may also be all about a certain part of your self you cannot control but you strive to subordinate to your reason.
Other possible interpretation of asphyxiation dreams is closely connected to your incapability of expressing your feelings in the waking life. Consequently, your feelings and emotions 'strangle' your subconscious and your dreams.