Humans wheeze and sneeze, pets itch and scratch. This is an over-simplification of allergy signs, but it holds fairly true.
Itch is the sensation that induces the need to scratch. It is produced by a complex interplay of chemicals, sensory nerve endings, and neural pathways. The inciting causes are numerous; the results are similar. Your pet scratches, licks, and chews at itself. Symptoms can vary from subtle (and clandestine) over-grooming and hair coat barbering by cats, to bleeding cuts and swollen ears in dogs. Horses can rub so vigorously, that their tail and mane hairs are broken off.
There are many causes of itch (called pruritus). The five most common are: