Thespis is credited as the first actor.
According to Aristotle, writing 200 years later, Thespis was born in Attica some time in the 6th century.Thespis originally sang dithyrambs, songs based on the myths of ancient Greece with choric refrains. Thespis introduced a new style of theater in which one person depicted one actor, distinguishing the different characters with masks. It's said that Thespis would walk around with a handcart and perform one man plays about the bad behavior of men.
The new style was called tragedy. In 543 BCE, a tragedy competition was held in City Dionysia. Thespis was the winner.
In homage to the first actor, actors call themselve Thespians. There's also a superstition that Thespis is a mischevious spirit that can help or harm a production, depending on his mood. Some groups just laugh it off while others do some sort of ritual to get Thespis to help them.
It should be noted that there is very little information on Thespis and the origins of Greek theater in general, so it's possible that Thespis's influence is exagerated.