Arges was an ally of the Titans who along with them was imprisoned deep beneath the sea of Tartarus by Zeus after their reign of destruction ended. After being freed by Hades he was ordered to find and kill Hercules and went smashing through Thebes, until Hercules reveals himself. Hercules had earlier made a deal with Hades that he would have his strength taken away for 24 hours so Arges takes his time beating him up badly. Phil comes to the rescue and convinces him that he doesn't need his strength to beat him and Arges picked Hercules up, deciding to finish him off by biting his head off. But thinking quickly Hercules shoves a torch into his eye blinding him and he stumbles around, Hercules uses this opportunity to tie Arges' feet together causing him to trip and fall off a cliff screaming to his death.
In the original mythology the Cyclopes race were imprisoned by Cronus, the king of the Titans, but in the film this Cyclops acts as an ally to the Titans.
In the Hercules animated series other Cyclopes were seen but they were not as large as this one. Some of them were no larger than a human with the exception being Echidna's children, a large blue two-headed "Bi-clops" and a large Cyclops.
It is possible that he is Polyphemus. And when Hercules blinds him, it could be a reference when Odysseus blinded Polyphemus. However, "Hercules and the Odyssey Experience" featured the Cyclops that Odysseus blinded, and blinded again this time by Odysseus's son.