A band of immensely powerful humanoid space travellers who visited ancient Earth and were worshipped as the gods of Greece, of whom Apollo was the last survivor on Pollux IV.
Apollo's people were humanoids able to channel great energies through their bodies, thanks to an extra organ in the chest noted by Doctor McCoy. About five thousand years ago they came to Earth and settled around the Mediterranean, where the early Greeks took them for gods; Apollo names Zeus, Hera, Athena, Artemis and others among them.
They are described in the Original Series episode Who Mourns for Adonais?. When humanity outgrew them they returned to Pollux IV, but they needed worship as others need food. One by one the others gave up and spread themselves upon the wind until only Apollo remained.
Apollo seizes the Enterprise and demands that the crew stay to adore him. Once the ship destroys the temple that is his source of power, he accepts that his time is over and fades away to join the rest.