Liberal democracy is a form of representative democracy where elected representatives that hold the decision power are moderated by a constitution that emphasizes protecting individual liberties and the rights of minorities in society, such as freedom of speech and assembly, freedom of religion, the right to private property and privacy, as well as equality before the law and due process under the rule of law, and many more.
Such constitutional rights (also named liberal rights) are guaranteed through various controlled institutions and various statutory laws. Additionally the constitution of most of the contemporary liberal democracies protects the rights of individuals and minorities, and prohibits the will of majority (majoritarianism), by almost eliminating that rule in practice.
Pros and cons
Some would argue that liberal democracy isn't democratic or liberal at all. They would argue that "liberal democracy" does not respect majority rule (except when citizens are asked to vote for their representatives), and also that its "liberty" is restricted by the constitution or precedent (in the UK) decided by previous generations. They would argue that, by prohibiting citizens the right to cast votes on all issues (especially for serious subjects like going to war, constitutional amendents or constitution abolishment etc.), this turns "liberal democracy" into the precursor of oligarchy.
Others would say that only a liberal democracy can guarantee the individual liberties of its citizens and prevent the development into a dictatorship. Unmoderated majority rule could - in this view - lead to an oppression of minorities.
The concept of an open society is closely related to liberal democracies. Since many liberals see democracies with strong statist reflections through the public choice theory as slow, dogmatic, conservative and not too apt for change, the liberal democracy contrasts with what could be called the "statist" democracy in that it emphasizes the civil society as the engine of its public discourse and development further.
All and all, liberal democrats often simply see the civil society as exactly the best way to satisfy the private, cultural and communitarian preferences of minorities (as well as majorities). Democratically supporting the arts, private communities, sports leagues or other assocations in the civil society is seen by them to boost the majorities' preferences, either willingly or unwillingly by the policy makers.
Relation to indirect democracy
All liberal democracies are representative democracies. Some of these democracies have additional systems of referenda to give the electorate a possibility to overrule decisions of the elected legislature or even to make decisions by plebiscite without giving the legislature a say in that decision. Switzerland is one of the few liberal democracies with a representative system combined with referenda and plebiscites. Other countries have referenda to a lesser degree in their political system. Adding referenda to a political system could help prevent the evolution of a liberal democracy into an oligarchy.
Australia, Canada, the member states of the European Union, Iceland, New Zealand, Norway and the United States are all examples of somewhat liberal democracies (though of course it is sometimes argued that none is perfect with respect to the above rights).