A parliamentary system of government means that the executive branch of government has the direct or indirect support of the parliament.This support is usually shown by a vote of confidence. The relationship between the executive and the legislature in a parliamentary system is called responsible government.rom Wikipedia, the free encyclopedia. States currently utilizing parliamentary systems are denoted in red and orange —the former being constitutional monarchies where authority is vested in a parliament, the latter being parliamentary republics whose parliaments are effectively supreme over a separate head of state.