Ara H 1, Ara H 2, and Ara H 3 are the three main peanut allergies. AH1 and AH2 are typically higher-acuity anaphylactic type reactions. The molecular cause for this is that some Immunoglobulin E develop a serum sensitivity and bind directly to vicilin and conglutin (the active proteins in AH1 and AH2). There are actually 7 or 8 Ara H complexes, but it is believed the remaining ones have a lesser affinity for IgE, reducing the frequency of allergic reactions and thus their availability for relevant studies.
The prevalence of the allergy is generally attributed to a combination of exposure and genetics. Many people have a genetic predisposition to certain allergies, but to a certain extent the body must be exposed to the allergen before an allergy will develop. The high use of peanuts in the food industry, and even to a lesser degree in skin care products like lotions, can account for early exposure resulting in allergies.
From the other direction, some research suggests that early and frequent exposure from infancy through childhood (albeit the choking risk) can reduce the demographic prevalence of an allergy in a given population.