Neutering an animal means removing its reproductive organs - the testicles in males and ovaries and uterus in females. This prevents them from producing young. This procedure also prevents many other things...
In females it stops their cycle and so no further seasons will be experienced. In females who are 6 months old and have not had a season,neutering will dramatically reduce the likelihood of mammarytumours in the future.
Neutering or spaying females also prevents pyometra. This is a life threatening illness where the uterus is infected, and has filled up with pus. Bacteria from this can get into the bloodstream and make your pet very ill very quickly and may die. Without prompt veterinary treatment, which involves spaying your pet whilst it's ill which increases the anaesthetic risk, your pet will deteriorate quickly.
Females may also experience false (phantom) pregnancies which in some bitches causes a lot of distress. This too is prevented by spaying.
By neutering males, you lower the testosterone levels. This will reduce behaviours such as mounting, urine spraying and some forms of male aggression. It is also less likely your pet will stray, as males have the desire to roam to find a female.
If you do not intend to breed from your dog neutering has undoubted advantages both in the male and the female.