In every Greek myth there is something supernatural about the myth. For example, the ancient Greek gods are featured in the myths or there are creatures like the hydra, Medusa or the Pegasus. In most Greek myths, intervention of the gods to solve a problem is the main supernatural element. It also has elements like super human strength, as is found in Hercules.
The ancient Greek myths follow the values and social cues which were common to the Greeks and their belief systems. The explanations of events were told using only the Greek context and culture.
The Greek myths sought to explain how the world came into being and how the natural world works. The myths would tell something about the earth in every story. For example, thunder storms were considered as the anger of Zeus or a toiling sea was the result of Poseidon's wrath. The stories would tell why the events of the natural world occurred using the gods or creatures.
The Greek myths told about human nature. The myths showed admirable strength in characters like Hercules, but also showed weaknesses. In the case of Hercules, he was not intelligent. Not only were humans given flaws, but even the gods in Greek myths were prone to mistakes and weakness. For example, many of the gods cheated on spouses. These flaws sought to explain human nature.
The Greek myths discussed dualities, such as light versus dark or good versus bad. These were not only explanations, but also lessons for the listener. In the myths, the dualities were often represented by various characters who represented one side of the problem. For example, Hercules was considered "good" while the monster he fought was considered "bad."