Phaethon was a name given to different figures in Greek mythology, but the best known was the son of the Oceanid nymph Clymene and either the god Apollo or Helios; both of those gods were associated with the sun. Some sources attribute different characters as his parents.
The myth has it that when Phaethon was challenged by his friends, he asked his mother if his father was really a god. Clymene reassured him that it was true and told him to ask his father directly. So, he asked Apollo (or Helios) to give him some proof that he was his son by linking him to the sun in some way. The young man asked that he drive the sun chariot for one day and his father agreed. However, when he was placed on the driver's seat, Phaethon was unable to control the horses; the Earth was about to be burnt up due to the misdriving of the sun's chariot. Afraid of this, Zeus decided to avoid the disaster and was forced to kill Phaethon with a thunderbolt.