Allergies trigger an unwarranted immune response. Take for instance a nut allergy, a random example. Upon exposure to some nut molecule, certain/specific naive B cells intercept this molecule as foreign and activate an army of mature Ab producing B cells (Plasma Cells). These B cells are then stimulated to produce a specific type of antibody (IgE), which bind to mast cells (contain histamine and heparin). At this point, nothing too serious happens.
It's upon secondary exposure to the allergen, that problems arise. The allergen binds to the IgE antibody causing mast cells to implode and release its contents. Histamine has specific receptors within various areas of the PNS and CNS that illicit different responses. Binding of histamine to one of these receptors (bronchial smooth muscle) is what ultimately causes bronchoconstriction, restricting air intake and making it difficult for the individual to breath.