This centerpiece was called the Orchestra, or the Dancing place. This is where action took part. Later, they added the Proskenion, an area specifically made for acting.
In a Greek theater, the round flat space where the action took place was called the orchestra.
The orchestra (meaning, "dancing space") had a circular shape. It was a level space where the chorus would sing, dance and even interact with the actors staying on the stage near the skene. The earliest orchestras were simply made of hard earth, but in the Classical period some orchestras were paved with marble and other materials. In the center of the orchestra you could see a thymele, or altar.