The role of mythology, in past times, was to explain the unknown. For example, if someone wanted to know why droplets of water were falling from the sky, where there obviously was no ocean, they would invent a supernatural reason for it. As time passed, and general knowledge grew, mythology evolved into something used for entertainment, or simply to pass the time. Now, in modern times, mythology is not only for the enjoyment of those who know of it, but also to analyze how ancient peoples thought or believed.
Back in ancient Greece, Mythology was used to explain origins, this includes everything from the city-states, to the geography of the area, to how and why civilized humans came to exist in the first place. One of the "mysteries" solved by Greek mythology is the inherent evil present in humans, which is explained by weaving the story of a woman created by the gods with an insatiable curiosity who was given a box that she was told not to open. The box contained all the evil inside of the souls of man. Pandora, the woman with the box, seeing the horror, closed the box before the one beneficial attribute escaped: hope. The Greeks had countless myths just like these, explaining something that they did not quite understand.
Today, The common person uses ancient mythology to entertain and enjoy. Perhaps to hone the art of storytelling. Those who have a job pertaining to it often use ancient mythology to better understand how people thought and acted in the past. Ancient Greeks used mythology for enjoyment as well, however they also used it as a valid historical and recent record. There are similarities between the two periods' usage of myths, but the main use differs so much it makes the similarities seem paltry.