Spaying is the surgical removal of female ovaries and uterus. Benefits include not having menses and no unwanted pregnancy. There are other health benefits which include prevention of fatal womb infections as well as mammary tumours.
A male having surgical removal of his testicles is called castration. This can prevent dominance aggression, mounting behaviour, prostate disease and perineal hernias. Additionally, there is decreased urine marking of territory and less wandering and fighting.
Like all things in life, there are pros and cons to doing this, and your doctor can discuss these with you.