Spay definition: An ovariohysterectomy, or spay, is a surgical procedure that involves removing the female reproductive organs (ovaries and uterus) so that a female animal can no longer have offspring.
Neuter definition: A castration or neuter is a surgical procedure that involves removing the male reproductive organs (testes) so that a male animal can no longer cause a female animal to produce offspring.
Cats
One female cat can produce an average of 4 to 6 kittens per litter and an average of 3 litters per year. By the age of three years old, a non-spayed cat can be responsible for up to 200 new cats in the world. There are not enough homes for this many cats. Most of these poor animals live their lives as ferals, without appropriate food or veterinary care. For this reason, they also serve to perpetuate many cat diseases that can affect our own well cared-for kitties. Non-neutered male cats not only contribute to the cat overpopulation problem, but are also more likely to be run over by cars or killed by wild animals, as they roam the countryside seeking out females. Most feral cats live a miserable existence of only 2 to 3 years.
Dogs
Dogs can produce almost as many unwanted puppies as cats can kittens. However, dogs are also very prone to developing disease situations due to not being spayed or neutered. Female dogs can develop life-threatening breast cancers and uterine infections. Male dogs can develop prostate infections, testicular cancers and cancerous anal areas. Brucellosis is a serious zoonotic disease that affects both male and female dogs as well as humans, and can be transmitted between dogs by breeding. This is a good article to read if you interested in a more thorough discussion on diseases that can be prevented by spaying and neutering your dog: