Monarchy refers to a system of government in which executive office is held by an individual for life who passes it to their child (or some other blood relative if s/he is childless) upon their death. In some instances monarchs hold absolute power (see Tsarist Russia), in other cases they are ceremonial figureheads and various states in between. Monarchy was among the first system of government to develop and has been around for most of the History of Civilization. The reasons for this are simple, someone who got to the top of an early society decided to pass the job onto his son, who latter followed his example in time. Since most trades were hereditary in the past, this was not seen as out of place and became traditional. For the last 200 years, monarchism has been on the decline being replaced by Republics and non monarchical Dictatorships.
Two related concepts are Nobility and Feudalism. Nobility are basically sub-monarchs: hereditary rulers who oversee smaller areas of territory and pledge their services to their monarch. A noble pledges his loyalty to the monarch, or a to higher-ranking noble in one of several tiers of nobility ultimately linked to the reigning monarch. Feudalism is a system of government based on a monarch and nobles, and it was fairly common historically, all though not universal for monarchies. For example Imperial China, after the Sui Dynasty, had a centralized monarchy run by bureaucrats selected by examinations.
Monarchies in Fiction
Most fantasy universes involve some form of monarchy, it being the dominant form of government in pre-modern times. While less common, monarchy is not an unusual form of government in science fiction.