Republicans believe that the best form of government is one in which decisions are made by a a council of citizen representatives. Classic historic examples of republican government include pre-imperial Rome and renaissance period Venice. In both cases the governing body was filled by a combination of heredity and appointment, representing not only the citizens but also powerful political and economic interest groups.
The most notable contemporary republic is the government of the United States of America which has a bicameral legislature selected by popular election under the rules established in its written constitution. The constitution is considered a republican document because it establishes a specific hierarchical process which minimizes direct popular involvement in the mechanisms of government and formalizes the delegation of policy making to elective representatives. The US constitution is available for reference from the National Archives. In the modern context one of the best explanations of republican government is found at the University of Chicago Press constitution resource site.
Republicans can also refer to members of the Republican Party, a political party which advocates republican government.