Democracy has been hanging around as an idea for about 4000 years. The idea behind it is that the people who are in a society, whether it is as small as the village bowls club to as large as the country of India¹,
decide who the people that run the society are. In this way they have some small control over what the governing body does on their behalf. The members of society vote for people that will best represent society's interests through their policies. If they do not do a good job they can be replaced at the next election. As people who run for these positions tend to want to keep them for a while, threatening to throw them out if they do a bad job makes sure that they do what you want, because if they don't then someone else will. The manner in which people are elected and thrown out varies from place to place but these are some of the more common ones:

First Past The Post

This system is currently in use for general pariamentary elections in the UK. Every person who qualifies to vote² has the option to choose just one candidate from a list of possibles. The candidate with the most votes is elected, they do not need a majority, just more votes than anyone else running.

Electoral Colleges

As in the USA with electing people to president.

Proportional Representation

European Elections

Automatic Transferral of Votes

Students union