Video: This by the American Chemical Society (ACSReactions on YouTube) details why peanut allergies are particularly dangerous and a new theory why peanut allergies have been on the rise. Peanuts have 13 unique proteins known to trigger allergy reactions, and these proteins aren't readily destroyed in your gut. That means the peanut proteins, once they get into your bloodstream, can still trigger allergic reactions after the food has been digested. So people with peanut allergies shouldn't let their guard down even a while after eating new foods if the ingredients and manufacturing process aren't known.
Also, for people with severe peanut allergies, even the tiniest bit of exposure -- inhaling peanuts or being touched by someone who had just eaten peanuts -- can cause a possibly life-threatening reaction.
As for why so many kids now have peanut allergies, scientists have found that kids who avoided peanuts at a young age actually were more likely to develop peanut allergies than those who were exposed to peanuts early on. That research is more fully described in this video. If you're expecting a child or have a young kid, this is something to discuss with the paediatrician, because, frankly, peanut allergies suck.