Presidents all over the world are not always normal executives like the president of India.
In many countries of the world ,the president is both the head of the state and the head of the government. The president of The United States of America is the most well-known example of this kind of president.
US President is directly elected by the people he probably choses and appoints all ministers. The law making is still done by the legislature the president can veto any law.
Most importantly the president does not need the support of the majority of members in the Congress and neither is he answerable to them. He has a fixed tenure of 4 year and complete sit even if his party does not have a majority in the Congress.
This model is followed in most of the countries of Latin America and many of the ex Soviet Union countries. Given the centrality of the president , this system of government is called the presidential form of government .In countries like ours that follows the British model the Parliament is Supreme .Therefore our system is called parliamentary system of government.