The title president is derived from the Latin prae- "before" + sedere "to sit." As such, it originally designated the officer who presides over or "sits before" a gathering and ensures that debate is conducted according to the rules of order (see also chairman and speaker), but today it most commonly refers to an executive official in any social organization. Early examples are from the universities of Oxford and Cambridge (from 1464) and the founding President of the Royal Society William Brouncker in 1660. This usage survives today in the title of such offices as "President of the Board of Trade" and "Lord President of the Council" in the United Kingdom, as well as "President of the Senate" in the United States (one of the roles constitutionally assigned to the vice president). The officiating priest at certain Anglican religious services, too, is sometimes called the "president" in this sense. However, the most common modern usage is as the title of a head of state in a republic.

In pre-revolutionary France, the president of a Parlement evolved into a powerful magistrate, a member of the so-called noblesse de robe ("nobility of the gown"), with considerable judicial as well as administrative authority. The name referred to his primary role of presiding over trials and other hearings. In the 17th and 18th centuries, seats in the Parlements, including presidencies, became effectively hereditary, since the holder of the office could ensure that it would pass to an heir by paying the crown a special tax known as the paulette. The post of "first president" (premier président), however, could only be held by the King's nominees. The Parlements were abolished by the French Revolution. In modern France the chief judge of a court is known as its president (président de la cour).

The first usage of the word president to denote the highest official in a government was during the Commonwealth of England. After the abolition of the monarchy the English Council of State, whose members were elected by the House of Commons, became the executive government of the Commonwealth. The Council of State was the successor of the Privy Council, which had previously been headed by the Lord President; its successor the Council of State was also headed by a Lord President, the first of which was John Bradshaw. However, the Lord President alone was not head of state, because that office was vested in the council as a whole.

The modern usage of the term president to designate a single person who is the head of state of a republic can be traced directly to the United States Constitution of 1787, which created the office of President of the United States. Previous American governments had included "presidents" (such as the president of the Continental Congress or the president of the Massachusetts Provincial Congress), but these were presiding officers in the older sense, with no executive authority. It has been suggested that the executive use of the term was borrowed from early American colleges and universities, which were usually headed by a president. British universities were headed by an official called the "Chancellor" (typically a ceremonial position) while the chief administrator held the title of "Vice-Chancellor". But America's first institutions of higher learning (such as Harvard University and Yale University) didn't resemble a full-sized university so much as one of its constituent colleges. A number of colleges at Cambridge University featured an official called the "president". The head, for instance, of Magdalene College, Cambridge was called the master and his second the president. The first president of Harvard, Henry Dunster, had been educated at Magdalene. Some have speculated that he borrowed the term out of a sense of humility, considering himself only a temporary place-holder. The presiding official of Yale College, originally a "rector" (after the usage of continental European universities), became "president" in 1745.

A common style of address for presidents, "Mr/Mrs. President," is borrowed from British Parliamentary tradition, in which the presiding Speaker of the House of Commons is referred to as "Mr/Mrs. Speaker." Coincidentally, this usage resembles the older French custom of referring to the president of a parlement as "Monsieur/Madame le Président", a form of address that in modern France applies to both the President of the Republic and to chief judges. Similarly, the Speaker of the House of Commons of Canada is addressed by francophone parliamentarians as "Monsieur/Madame le/la Président(e)". In Pierre Choderlos de Laclos's novel Les Liaisons Dangereuses of 1782, the character identified as Madame la Présidente de Tourvel ("Madam President of Tourvel") is the wife of a magistrate in a parlement. The fictional name Tourvel refers not to the parlement in which the magistrate sits, but rather, in imitation of an aristocratic title, to his private estate.

Once the United States adopted the title of "president" for its republican head of state, many other nations followed suit. Haiti became the first presidential republic in Latin America when Henri Christophe assumed the title in 1807. Almost all of the American nations that became independent from Spain in the early 1810s and 1820s chose a US-style president as their chief executive. The first European president was the president of the Italian Republic of 1802, a client state of revolutionary France, in the person of Napoleon Bonaparte. The first African president was the President of Liberia (1848), while the first Asian president was the President of the Republic of China (1912).

In the twentieth and twenty-first centuries, the powers of presidencies have varied from country to country. The spectrum of power has included presidents-for-life and hereditary presidencies to ceremonial heads of state.

Presidents in the countries with a democratic or representative form of government are usually elected for a specified period of time and in some cases may be re-elected by the same process by which they are appointed, i.e. in many nations, periodic popular elections. The powers vested in such presidents vary considerably. Some presidencies, such as that of Ireland, are largely ceremonial, whereas other systems vest the president with substantive powers such as the appointment and dismissal of prime ministers or cabinets, the power to declare war, and powers of veto on legislation. In many nations the president is also the commander-in-chief of the nation's armed forces, though once again this can range from a ceremonial role to one with considerable authority.

Presidential systems

In almost all states with a presidential system of government, the president exercises the functions of head of state and head of government, i.e. the president directs the executive branch of government. When a President not only is head of state, but also head of government, is this, in Europe known to be a President of Counsel from the French Présidente du Conseil, used 1871-1940 and 1944-1958, as the Third and Fourth French Republics. In the United States the President has always been both Head of State and Head of Government and has always had the title of President.

Presidents in this system are either directly elected by popular vote or indirectly elected by an electoral college or some other democratically elected body.

In the United States, the President is indirectly elected by the Electoral College made up of electors chosen by voters in the presidential election. In most states of the United States, each elector is committed to voting for a specified candidate determined by the popular vote in each state, so that the people, in voting for each elector, are in effect voting for the candidate. However, for various reasons the numbers of electors in favour of each candidate are unlikely to be proportional to the popular vote. Thus, in five close United States elections (1824, 1876, 1888, 2000, and 2016), the candidate with the most popular votes still lost the election.

In Mexico, the president is directly elected for a six-year term by popular vote. The candidate who wins the most votes is elected president even without an absolute majority. The president may never get another term. The 2006 Mexican elections had a fierce competition, the electoral results showed a minimal difference between the two most voted candidates and such difference was just about the 0.58% of the total vote. The Federal Electoral Tribunal declared an elected president after a controversial post-electoral process.

In Brazil, the president is directly elected for a four-year term by popular vote. A candidate has to have more than 50% of the valid votes. If no candidates achieve a majority of the votes, there is a runoff election between the two candidates with most votes. Again, a candidate needs a majority of the vote to be elected. In Brazil, a president cannot be elected to more than two consecutive terms, but there is no limit on the number of terms a president can serve.

Many South American, Central American, African and some Asian nations follow the presidential model.

Semi-presidential systems

A second system is the semi-presidential system, also known as the French model. In this system, as in the parliamentary system, there are both a president and a prime minister; but unlike the parliamentary system, the president may have significant day-to-day power. For example, in France, when his party controls the majority of seats in the National Assembly, the president can operate closely with the parliament and prime minister, and work towards a common agenda. When the National Assembly is controlled by his opponents, however, the president can find himself marginalized with the opposition party prime minister exercising most of the power. Though the prime minister remains an appointee of the president, the president must obey the rules of parliament, and select a leader from the house's majority holding party. Thus, sometimes the president and prime minister can be allies, sometimes rivals; the latter situation is known in France as cohabitation. Variants of the French semi-presidential system, developed at the beginning of the Fifth Republic by Charles de Gaulle, are used in France, Portugal, Romania, Taiwan, Sri Lanka and several post-colonial countries which have emulated the French model. In Finland, although the 2000 constitution moved towards a ceremonial presidency, the system is still formally semi-presidential, with the President of Finland retaining e.g. foreign policy and appointment powers.

Parliamentary systems

The parliamentary republic, is a parliamentary system in which the presidency is largely ceremonial with either de facto or no significant executive authority (such as the President of Austria) or de jure no significant executive power (such as the President of Ireland), and the executive powers rests with the Prime Minister who automatically assumes the post as head of a majority party or coalition, but takes oath of office administered by the president. However, the president is head of the civil service, commander in chief of the armed forces and in some cases can dissolve parliament. Countries using this system include Austria, Albania, Bangladesh, Czech Republic, Germany, Greece, Hungary, Iceland, India, Ireland, Israel, Italy, Malta, Pakistan, Singapore.

A variation of the parliamentary republic is a system with an executive president in which the president is the head of state and the government but unlike a presidential system, is elected by and accountable to a parliament, and referred to as president. Countries using this system include Botswana, South Africa and Suriname.

Collective presidency