At the center of the square is a statue of King Philip IV, a king that was crowned at an early age and was in charge of many wars, who impoverished and weakened Spain.
Plaza de Oriente, located to the east of the Royal Palace, was established by the King of France, Joseph Bonaparte, Napoleon's brother. He tried to help the city and invest in it. Not that this helped him since most of the residents of Madrid hated him.
Today, the square is open only to pedestrians, which make it a really nice place. If you come to Madrid in the summer, try going for an evening walk and enjoying the square's full glory.