Shah (Persian: شاه), from the Avestan word khshathra "king", is the Persian term for a monarch and used by the former rulers of Persia (present-day Iran) as well as the rulers of the Persian Empire. The title roughly translates as Emperor in English as the monarch of Persia was technically the Emperor of the Persian Empire (later the Empire of Iran as Iran was officially known until 1979).
The last Shah of Iran, Mohammed Reza Pahlavi officially adopted the title Shahanshah (Persian: شاهنشاه) - literary King of Kings or Emperor during his coronation. He also styled his wife Shahbanou (Persian: شهبانو) or Empress (previously the wife of the Iranian monarch was known as Maleke (Persian: ملکه) or Queen).
Shah is also a common last name among people from India, especially the state of Gujarat. It usually indicates the person or previous generations were involved in business or trade, and is unrelated to the above meaning of King.