Zeus is the king of the Greek Gods and the ruler of Olympus.
Thousands of years ago, Zeus led the Olympians in their war against the Titans. However, Hades, Zeus' brother, made a pact with the Titans, and, with the unwitting help of his lover Hippolyta, betrayed the Olympians to the Titans. The Titans were defeated and Zeus banished Hades to Tartarus. Hippolyta was commanded to forever guard the gates of Tartarus for her unwitting role in the betrayal.
In the 21st century, Felix Faust overthrew Hades, threatening the balance between order and chaos. To prevent this, Zeus decreed that Wonder Woman was to go to Tartarus, defeat Faust, and restore Hades to the throne. To this day, a deluded imposter named Maximillian Zeus impersonates him.
Zeus' role in DC Comics is quite similar to his role in the Greek myths. Zeus, son of Kronos and Rhea, overthrew his parents, the Titans, and ruled Olympus. He married his sister, Hera, and he had many children, but only a fraction of them with Hera. Ares and Hephaestus were Hera's; Hermes' mother was Maia, Athena's mother Metis. He also had many children with Themis.