Antaeus, son of Gaia and Poseidon, was a Libyan giant whose strength appeared invincible. He challenged all passers-by to a wrestling match that he invariably won. Upon winning, he slaughtered his adversaries. That is until he met Hercules.
Antaeus Challenges Hercules
Hercules had gone to the garden of the Hesperides for an apple. (The Hesperides, daughters of Night or the Titan Atlas, took care of the garden.) On Hercules' way back, the giant Antaeus challenged the hero to a wrestling match. No matter how many times Hercules threw Antaeus off and tossed him to the ground, it did no good. If anything, the giant appeared rejuvenated from the encounter.
The Strength of Antaeus From His Mother Gaia
Hercules eventually realized that Gaia, the Earth, Antaeus' mother, was the source of his strength, so Hercules held the giant aloft until all his power had drained away. After he killed Antaeus, Hercules proceeded safely back to his taskmaster, King Eurystheus.
Incidentally, the modern American hero and demigod Percy Jackson, in the eponymous series, written by Rick Riordan, also defeats Antaeus by suspending him above the earth.
Ancient Sources for Antaeus
Some ancient writers who mention Antaeus are Pindar, Apollodorus, and Quintus Ancient Sources for Antaeus Smyrnus.