Anaphylaxis can kill you. And do so very quickly and unexpectedly.
Our immune system protects us every minute of every day by attacking microscopic creatures that could do us harm. Things such as viruses, bacteria, and other invaders. When a foreign organism enters our body, the immune system recognizes it and immediately goes to work building antibodies against it. These antibodies attach to the foreign organism and attract various blood cells to it. Mostly the various types of White Blood Cells (WBCs) we all have. The cells then damage and devour the invader. That's a good thing.
But sometimes this protective system goes haywire. It over-reacts. It creates substances that lead to an acute asthmatic attack, a diffuse rash, a swelling of the face and hands and feet and other body parts, and a dramatic, and often deadly, drop in blood pressure. We call such an overwhelming reaction anaphylactic shock.
The treatment for anaphylaxis is the immediate injection of epinephrine, antihistamines, and steroids. These either block the allergic reaction itself or mitigate the body's reaction to it. But time is critical. These measures must be taken very quickly. This is why many people who have serious allergies carry small epinephrine injectors such as EpiPen.
Someone who is allergic to things such as bee stings, peanuts, certain foods or plants, or some medications can suffer such a reaction even if exposed to very small quantities of the allergen. A little dab can set off a major reaction.
Case in point: Myriam Ducre-Lemay.
Myriam was allergic to peanuts. She avoided them like the plague. But one evening, her boyfriend kissed her after he had eaten peanut butter and this set off an anaphylactic reaction that took her life.
Mayo Clinic Article: http://www.mayoclinic.org/diseases-conditions/anaphylaxis/basics/definition/con-20014324
Wikipedia Article: https://en.wikipedia.org/wiki/Anaphylaxis