A presidential system is a system of government where an executive branch

Executive (government)

Executive branch of Government is the part of government that has sole authority and responsibility for the daily administration of the state bureaucracy. The division of power into separate branches of government is central to the idea of the separation of powers.In many countries, the term...

 exists and presides (hence the name) separately from the legislature

Legislature

A legislature is a kind of deliberative assembly with the power to pass, amend, and repeal laws. The law created by a legislature is called legislation or statutory law. In addition to enacting laws, legislatures usually have exclusive authority to raise or lower taxes and adopt the budget and...

, to which it is not responsible and which cannot, in normal circumstances, dismiss it.

Although not exclusive to republic

Republic

A republic is a form of government in which the people, or some significant portion of them, have supreme control over the government and where offices of state are elected or chosen by elected people. In modern times, a common simplified definition of a republic is a government where the head of...

s, and applied in the case of semi-constitutional monarchies

Monarchy

A monarchy is a form of government in which the office of head of state is usually held until death or abdication and is often hereditary and includes a royal house. In some cases, the monarch is elected...

 where a monarch

British monarchy

The monarchy of the United Kingdom is the constitutional monarchy of the United Kingdom and its overseas territories. The present monarch, Queen Elizabeth II, has reigned since 6 February 1952. She and her immediate family undertake various official, ceremonial and representational duties...

 exercises power (both as head of state

Head of State

A head of state is the individual that serves as the chief public representative of a monarchy, republic, federation, commonwealth or other kind of state. His or her role generally includes legitimizing the state and exercising the political powers, functions, and duties granted to the head of...

 and chief of the executive branch of government) alongside a legislature, the term is often associated with republican systems in the Americas

Americas

The Americas, or America , are lands in the Western hemisphere, also known as the New World. In English, the plural form the Americas is often used to refer to the landmasses of North America and South America with their associated islands and regions, while the singular form America is primarily...

.