How would the ancient Greeks define a hero?

They were a pretty selfish bunch, often with additional antisocial tendencies thrown into the bargain--in other words, not exactly role models for the younger generation of today. But knowing their names and exploits is essential for understanding references in literature and even popular culture today. So let's recognize and celebrate Hercules and Perseus and the others by their proper dictionary definition: "In mythology and legend, a man or woman, often of divine ancestry, who is endowed with great courage and strength, celebrated for his or her bold exploits, and favored by the gods."