An allergy is an immune response to a foreign substance. This can be a food, pollen, pet, mold, bee sting etc.
On exposure to these substances, the immune system reacts by releasing proteins called antibodies. Things that cause antibodies to be released are called antigens or allergens.
Two types of antibodies are commonly produced: IgE (immunoglobulin E) and IgG (immunoglobulin G). Depending on the type of antibody your body produces, you may have more of an allergic type reaction or a sensitivity type reaction. It's possible to have both at the same time, and both can cause distinct as well as compounded symptoms.