The human equivalent is an ovario-hysterectomy. Females who have been spayed cannot have babies. They no longer secrete the hormones that regulate their reproductive readiness. Heat cycles bring hormonal changes that can lead to personality changes. Neutering refers to the surgical removal of a male companion animal's testicles.
Castration is another term for the same thing.
Males who have been neutered cannot manufacture sperm. In reality, neutering a male is similar to spaying a female. Female dogs go into heat every six months usually starting at six months of age. Dogs and cats are pregnant for 63 days. Nursing dogs and cats CAN get pregnant.