Democracy comes from the Greek words "demo", which means people, and "kratos", which means power. Democracy is a style of government in which the country is ruled by the people.
Participatory democracy is when the people directly have an influence over what happens in the government. For example, a meeting in a small town is called, and most of the population shows up to discuss changes, like building a new intersection or installing a traffic light.
This style of government is good for small towns, but imagine how hard it would be for most of the population of the United States to show up in Washington, DC to talk about a new law.
Elite democracy is a form of democracy in which a few elites, usually rich, well-educated people, influence political decisions. This is basically the opposite of participatory democracy.
This style of government is used in the electoral college, a small group of people who serve as a check on the potential tyranny of the majority. In the United States' history, the electoral college elected a president different from the one the people chose five times.
Pluralist democracy is the most obvious form of democracy in American government. This type of government is based on political parties that represent different people's wishes. These political parties compete to influence politics.
The most obvious example of this type of democracy are the political parties in the United States, the Democrats, and the Republicans. They try to get people on their sides to be able to win elections, and stand up for different political agendas.