President (from Latin pre "before" + sedere "to sit") is a title with varying functions. In government, the head of state of a republic. Actual powers vary, in some countries being a largely ceremonial head of state with the prime minister being the head of government and functioning as the chief executive officer.
A "presidential system" is typically one where the chief executive is directly elected and combines the role of head of state and head of government. A "parliamentary" system separates the roles, with the more ceremonial head of state typically being a non-hereditary president or a hereditary monarch.