The form of government in which citizens have the right to vote and elect officials is known as a representative democracy (or indirect democracy). In this system, elected representatives make decisions and pass laws on behalf of the citizens. Citizens typically exercise their voting rights during regular elections to choose their representatives at various levels of government.
Another related form is direct democracy, where citizens vote directly on laws and policies rather than electing representatives to make those decisions for them. However, direct democracy is less common in large, complex societies and is often used in smaller communities or for specific issues.
In practice, most modern democracies operate as representative democracies, with elected officials accountable to their constituents through regular elections.