Perseus is the son of Zeus, the king of the Greek gods, and a mortal woman. The woman's husband, Polydectes, king of Seriphos, was naturally angry, but when your wife has an affair with a god, what can you do? So, instead, when Perseus grew up Polydectes sent him on what he believed was an impossible quest. The king sent his step-son out to kill Medusa, one of three sisters called the Gorgons who were so ugly, anyone who looked at them would turn to stone. He appealed to the gods for help and was given a mirrored shield by Athena, the goddess of wisdom, and a pair of winged sandals by Hermes (also know as Mercury), the messenger of the gods. Perseus flew using the sandals to find Medusa. When he found her, he did not look at her. Instead, he used the reflection in the shield to guide his sword so he could behead her as she slept. As she died, the white, winged horse Pegasus sprang from her neck.
On his way back from his victory against the Gorgons, Perseus came across a woman chained to a rock, waiting to be sacrificed to a sea monster, called either Cetus or Draco, depending on which version of the myth you believe. This woman was Andromeda, the Princess. Her mother, Cassiopeia boasted that she and her daughter were more beautiful than the Nereids (or sea nymphs), which were the daughters of Poseidon (or Neptune), the god of the sea. Angered by the insult to his daughters, Poseidon sent floods to the lands ruled by Cassiopeia and her husband, King Cepheus. Cepheus consulted an oracle who told him that the only way to quell Poseidon's anger was to sacrifice his daughter.
Luckily, Perseus came on the scene just in the nick of time and killed the sea monster and saved the princess.
As a small side note, it is interesting that Cepheus shows up again in Greek mythology when he and 17 of his sons were killed by Hercules.