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The Cyclops (plural is cyclopes) is a species of Giant from Classical Mythology, characterized for only having a single eye set in their forehead. They were fairly
unimportant figures; Cyclopses were said to be responsible for forging Zeus's thunderbolts, and it was the curse of Polyphemus, a cyclops and son of Poseidon, for his blinding that led to the famous travels of Odysseus.
Cyclopes don't have much of an important history in most fantasy games. They do show up, but they tend to be just sort of... "there". Back in the day, Advanced Dungeons & Dragons basically portrayed them as little more than "slightly tougher Ogres with only one eye", and that's more or less been their highlight.
In 3.5e, the book Forgotten Realms: Shining South made them playable. They were actually one of the least unusual monsters to be playable in Third Edition.
In 4e D&D, Cyclopes were re-imagined with a more mystical nature; they were the Feywild equivalent of Ogres, and had magical powers, but were also highly disciplined and fanatically loyal servants of the Fomorians, deformed fae giants who sought to conquer the Feywild.
In Pathfinder, Cyclopes are the last remains of a once-mighty mystical empire that ruled through its mastery of prophecy and divination. When such magic stopped working right, they fell from power, and they are swiftly falling into decline as they devolve into barbarism. Pathfinder also features the "Great Cyclops", a rampaging brute of a cyclops based on the famous Ray Harryhausen cyclops from his 1950s film "The 7th Voyage of Sinbad". As a result, their entry in the Inner Sea Monster Codex included two new Oracle curses, the Curse of Hunger and the Curse of Powerless Prophecy, and a new Oracle archetype, the Cyclopean Seer.
The Iron Kingdoms features them as a race of clairvoyant giants, enslaved by the Skorne Empire and used as warbeasts in its armies. They tend to have animi representing their psychic powers, and to be weaker but better-armed and better-trained than the suite of Skorne heavies, comprising the bulk of the Skorne's light warbeasts. Molik Karn, their former ruler and their Archdominar's personal bodyguard and assassin, is their sole heavy, and as a warbeast with Weapon Master, is a bad motherfucker.
Monstergirl versions of these creatures are surprisingly popular in Japan. There, they tend to be more commonly seen in the form of "Monoeyes", which are basically non-giant sexy humans with one huge eye. This may be because Japan has quite a variety of one-eyed human-sized monsters in its mythology, which naturally crosses with the country's deviant love of sex. The Monster Girl Encyclopedia portrays them as one-eyed ogre-sized (if that) mamono with a single horn on their forehead; supposedly, they used to be giants, but shrank as part of the transformation into monstergirls. They are what Japanese call the "kuudere" archetype; stoic-faced and emotionless acting, but secretly very loving and passionate. They are renowned for their skill at crafting magical weapons, and often trade the gift of one of these rare and prized items in exchange for a night of sex to father a daughter.