How ignorant can you get? Before making a comment as stupid as the one you just made "Has anyone died of a peanut allergy from airlines serving nuts? I don't think so.", do a little research. Check out the Peanut Allergy website http://www.peanutallergy.com/bbpage.htm
before you say another word... it'll really open your eyes.
Personally I don't know of any incidents in which a person who served peanuts on an airplane died, but people the world over have died from ingesting peanuts, that's a fact. People who have died from being allergic to peanuts have suffered what's called anaphylactic shock (which I've put the definition below). The problem with being on an airplane is that the environment is closed, and of course you're 30,000-40,000 feet in the air. When one is on the ground and gets an allergic reaction, they need to get to the hospital right away. Getting to a hospital when you're in the air is of course very unlikely.
People have varying sensitivity levels to peanuts/nuts whatever. Usually it's divided into ingestion, the touch, or breathing of the food allergen. For some people their peanut allergy is so bad that if they touch a peanut or yes, breathe 'peanut dust', they will have a reaction. You asked what that was - have you ever seen the crumbs at the bottom of a jar of peanuts or a box of cereal? A lot of those particles are so small they can get in the air very easily.
definition of anaphylactic shock (n-f-lktk shk)
A sudden, severe allergic reaction characterized by a sharp drop in blood pressure, urticaria, and breathing difficulties that is caused by ingestion of an allergic food or the injection of a foreign substance, such as a drug or bee venom, into the body after a preliminary or sensitizing ingestion or injection. The reaction may be fatal if emergency treatment, including the administration of epinephrine injections, is not given immediately. Also called anaphylaxis.