Eugene Volokh of the UCLA School of Law notes that the United States exemplifies the varied nature of a constitutional republic—a country where some decisions (often local) are made by direct democratic processes, while others (often federal) are made by democratically elected representatives.
Answer: The United States is a representative democracy, AKA republic, because the citizens do not vote directly on laws. Rather, they elect representatives (the House of Representatives and the Senate) to vote on laws for them. If it were a direct democracy, every law would be voted on by anyone who cared to.