Authoritarian governments exercise unlimited power, while democratic governments are run by the will of the people and feature regular elections. Some governments have traits of both styles.
Historically, the majority of governments were authoritarian. Ruled by a monarch, despot or dictation, these governments had virtually unlimited power. However, popular revolt was almost always a possibility, so leaders had to ensure that they did not push their citizens too far. In addition, aristocratic classes often held considerably sway, and upsetting the wealthy frequently led to coups.
Democracy began to flourish after it was implemented in the United States, and it is now popular throughout the world. Democratic governments allow citizens to choose the leaders in control of the government, and most democracies have constitutions that limit government power. However, this does not always guarantee human rights or effective policy. Slavery in the United States, for example, continued for nearly 100 years after a democratic government was created.
Some governments are a mix between these two types. While China has elections, all candidates running for election must be members of the Communist party or granted permission by the party. In addition, those is positions of power in China have only limited powers.