You must first understand the Greek concept of hubris to understand the story of Sisyphus. The modern definition of hubris is the trait of excessive pride. To the Greeks, hubris was not only being prideful, but prideful to the point of thinking yourself better than, or at least outside the control of, the gods. Hubris was a major plot point in many Greek stories, such as Oedipus Rex, who thought he could escape the fate laid out for him by the gods. The Greek gods punished hubris mercilessly, leading to the concept of the tragic hero who struggles vainly against that which he cannot hope to overcome.
Sisyphus was one of the craftiest men in the world, according to myth. He was born the son of the king of Thessaly and went on to found his own kingdom in Corinth. Sisyphus betrayed a secret of Zeus, who had kidnapped the beautiful daughter of a river god. Zeus ordered Sisyphus be chained to a stone in the underworld by Thanatos, the god of death, but Sisyphus tricked Thanatos into lying on the rock and chained him down. Thanatos was eventually freed by either Hades or Ares. Several more attempts to hold Sisyphus in the underworld failed, until he was finally tasked with pushing a boulder up a hill. Before reaching the top, the boulder always slips from his grasp and rolls back down.
Albert Camus wrote an interpretation of Sisyphus's story called "The Myth of Sisyphus," in which he called Sisyphus an "absurd hero." Camus interprets Sisyphus' struggle as being analogous to the futility of living, in that no matter how hard you work in life, at the top you lose your grip and it all means nothing. Camus argues there is absurdity in life and that, once someone embraces that absurdity, they can truly live. Sisyphus' title of absurd hero comes from his great love of life, and constant attempts to resist the grim inevitability of death.
The term "pushing a rock up a hill" is one that survives as a modern idiom and refers directly to the story of Sisyphus. Pushing a rock up a hill is synonymous with some futile and unpleasant task, often a punishment for something. It can be applied to a wide range of real-life scenarios, such as weight loss, "I run every day and I don't lose a pound, I'm just pushing a rock up a hill here." These scenarios are commonly referred to as "Sisyphean Tasks."