Representative democracy is a form of government founded on the principles of popular sovereignty by the people's representatives. The representatives form an independent ruling body (for an election period) charged with the responsibility of acting in the people's interest, but not as their proxy representatives—i.e., not necessarily always according to their wishes, but with enough authority to exercise swift and resolute initiative in the face of changing circumstances. It is often contrasted with direct democracy, where representatives are absent or are limited in power as proxy representatives.
The representatives are chosen by the majority of the voters (as opposed to the majority of the population/eligible voters) in elections. While existing representative democracies hold such elections to choose representatives, in theory other methods, such as sortition (more closely aligned with direct democracy), could be used instead. Also, representatives sometimes hold the power to select other representatives, presidents, or other officers of government (indirect representation).
An independent judiciary, which may have the power to declare legislative acts unconstitutional (e.g. Supreme Court) It may also provide for some deliberative democracy (e.g., Royal Commissions) or direct democracy measures (e.g., initiative, referendum, recall elections). However, these are not always binding and usually require some legislative action - legal power usually remains firmly with representatives.
In some cases, a bicameral legislature may have an "upper house" that is not directly elected, such as the Canadian Senate, which was in turn modelled on the British House of Lords.