Presidentialism

A presidential system is a system of government where a head of government is also head of state and leads an executive branch that is separate from the legislative branch. The United States, for instance, has a presidential system. The executive is elected and often titled "president" and is not responsible to the legislature, which cannot in normal circumstances dismiss it. The legislature may have the right in extreme cases to dismiss the executive, often through impeachment; however such dismissals are seen as so rare as not to contradict a central tenet of presidentialism, that in normal circumstances using normal means the legislature cannot dismiss the executive.

The title president has persisted from a time when such person personally presided over the governing body, as with the US President of the Continental Congress, prior to the executive function being split into a separate branch of government.

Presidential systems are numerous and diverse, but the following are generally true:

Countries that feature a presidential system of government are not the exclusive users of the title of President. For example, a dictator, who may or may not have been popularly or legitimately elected may be and often is called a president. Likewise, leaders of one-party states are often called presidents. Most parliamentary republics have presidents, but this position is largely ceremonial; notable examples include Germany, India, Ireland, Israel and Italy. The title is also used in parliamentary republics with an executive presidency, and also in semi-presidential systems.

...
Wikipedia