Most democratic countries hold new elections for their national legislature every few years. In a Parliamentary system the legislature chooses the leaders of the government. Some democracies elect other national officials (such as a president). Many democratic countries also have regional, provincial or state elections.
There are different ways to organize an election in different countries. Voters might vote for an individual, or they might vote for a political party (party list). This is because different countries use different voting systems.
Countries that are not democracies can also hold elections. This is usually done to let the people choose a local representative (like a mayor). Also many countries call themselves democracies, but behind the scenes have a more autocratic form of government.
Psephology is the study of elections.