An allergy is a physical reaction to some specific food or substance. If you have an allergy to cats, they'll make you itchy and swollen no matter how much you love to pet them.
If you have an allergy, it can range from mild — itchy eyes in the springtime — to serious — being unable to breathe after eating a peanut. People have allergies to all kinds of things, including milk, chocolate, corn, dust, mold, and just about any kind of animal you can think of. Allergy was originally Allergie, a German word invented by a doctor who combined the Greek roots allos, "other, different, or strange," and ergon, "activity."