What is a representative democracy?

Nearly all democracies are of this kind. The adult citizens elect resprentatives: they don't govern themselves directly. Only very small communities can govern themselves directly ("direct democracy") but even then it is often difficult. Three of the least populous Swiss cantons have something close to direct democracy. In Canton Glarus, for example, the laws made by representatives are initially only provisional. Once a year all the adult citizens meet in the capital and vote to confirm or reject the previous year's provisional laws. I wonder if that would work in any state of the U.S.? A referendum, if the result is binding, would also be a form od direct democracy.