A monarchy is a type of government where a group of people, that normally represents a dynasty, controls the country. The head of the group is known as the monarch. Normally the power is passed down the line to all of the blood relatives, normally made up of kings and queens.
A Democracy is a government in which power is held by the people, who exercise power directly or through elected representatives. There are many different types of Democracy's such as Direct Democracy and Representative Democracy.
An Oligarchy is a government in which the ruling power is in the hands of a few people. These types of governments don't normally work out.
An Aristocracy is a form of government that gives power to a small group of people, normally of high social standing, privileged group of people. It is not to be confused with a Monarchy.