Monarchy is the rule by one person, generally the King. Other titles are sometimes used; Emperor, Ayatollah or Shah, for example. In some cases, a democratic or republican title is used in place of a monarchical title; many absolute rulers style themselves as "President" even though they rule as kings. North Korea, for example.
A "constitutional monarchy" is a democratic or republican form of government which rules with or at the direction of the monarch; the United Kingdom of England, Scotland and Wales, for example. An "absolute monarchy" is a government in which all power is concentrated in the hands of the monarch.