Specifically, a federal democratic republic. There's no contradiction between "republic" and "democracy". "Republic" refers to sovereignty (the people hold sovereignty rather than a monarch), while "democracy" refers to power (the people hold power rather than a dictator).

Some democracies are not republics--the UK is a constitutional monarchy. Some republics are not democracies--the Roman Republic was an oligarchy and to some extent the early United States was, too.