This article is from the Children Allergies and Asthma FAQ, by Eileen Kupstas Soo email@example.com with numerous contributions by others.
Essentially the same thing that causes all allergies -- the immune
system. Some people produce antibodies in response to some substances.
When this happens, the person becomes allergic to the substance.
When the substance is introduced into the body at later times, there
will be a more or less severe allergic reaction. In the case of
insect allergies (or more correctly, insect *venom* allergies), the
substance is the venom injected by the insect when it stings.