President

A president is the leader and head of state of a country which is a republic. A president is usually elected directly through a vote by the citizens or indirectly by legislatures (parliaments) who were voted by the citizens and which represents them.
Some presidents are both the head of state and head of government, such as the President of the United States. In other countries, such as the Republic of Ireland, the President has a ceremonial role while the Prime Minister is the leader of the government. In France, the President and Prime Minister both share executive powers.
A president could also be the title of the head of a large business, company or organization.
Electing a President
Many republics have direct elections by citizens to elect a president. But some other republics do not. The President of the United States is elected by the electoral college. Some other republics choose a president this way. In some other republics, the parliament elects a president.
Countries that have a monarch as leader, are called monarchies. Some countries have neither a president or a monarch as leader, such as the Vatican City which is ruled by a religious leader called a Pope.
Companies also have presidents. They are elected by the people who own part of the company. In some companies, the people who are workers for the company elect (vote for) their company president.
Power of a President
The president of a country is not the same thing as a prime minister. A prime minister is part of a parliament, but a president is not. In some countries, (such as the United States or France), the president has more power and responsibility than anyone else. Such a president is often called the nation's chief executive. As chief executive, the president must take an active role in all phases of government. The republics where the president is both the head of state and head of government (and there is no prime minister) are called a presidential republics.
In other republics (such as India, Israel or the Republic of Ireland), to be president is more of an honor or a symbol, and the position has no real power. The real power in such republics is held by the prime minister, who is the head of government. In this kind of republics, the president is only the head of state, and are called parliamentary republics.
In some republics (such as France or Russia) both the president as the head of state, and the prime minister as the head of government, run the day-to-day affairs of the state, but often the president has more powers than the prime minister. Such republics are called semi-presidential republics.
Most monarchies that have a king or queen as their monarch and head of state, have no president, but very few monarchies, such as the United Arab Emirates has a president who is the head of state, who by custom (but not by law) is always the emir (monarch) of Abu Dhabi, which is de facto hereditary.
The American President is restricted by the written United States Constitution, which was written to make sure that the American executive never became as powerful as in the British system. The British Prime Minister is part of both the Legislature and Executive, whereas the American President is the head of the Executive. The American governmental system shows a clear separation of powers unlike the British system.
All the president's ministerial appointments have to be vetted by Congress (Parliament) and Congress may have an opposition majority.
The president does not have the ability to introduce and influence legislation in the same way as the British prime minister.
Congress has much greater control over the budget and foreign policy than the British Parliament.
There are broad areas of American life, such as education, crime and punishment, over which the president has virtually no influence at all.
The president even has very limited control over the economy.
So despite having a large nuclear arsenal, the American president can not carry out policy and introduce legislation as freely as the British prime minister.