Typically, an immunological reaction to a harmless
antigen - the body's
immune system mistakenly launches a response when none is needed.
Since this reaction involves all the usual factors; heat, pain, redness and swelling (the body tends to fight fire with fire), the effects can be quite serious, ranging from a sniffle to full blown anaphylactic shock.
some examples:
Hay fever
penicillin intolerance
Nuts
bee stings, wasp stings
a really serious allergic reaction can stop the heart, a situation which can be resolved with an injection of adrenalin, like in Pulp Fiction
I may well be wrong about all of the above. Please do not hesitate to flame / correct me.