To put quite simply, a character or creature that only has one eye naturally.
Monocular vision is symbolic of metaphorical narrow vision and lack of depth perception. As such, many human villains have one eye as an indication of their simplistic worldview. This also provides an excuse for an Eyepatch of Power. Characters who lack perspective on a temporary basis might sport Peek-a-Bangs or some other occular obtrusion.
It should be noted that Cyclops more accurately translates to "circle-eye" or "wheel-eye", referring to its size. Therefore Cyclopean technically means huge, and not one-eyed (not to mention Cyclopes themselves were giants).
Not to be confused with the Faceless Eye, cyclopes have a recognizable facial structure, with at least a mouth.
For other deviations from normal eye structure, see Eyeless Face, Third Eye, Oculothorax, and Extra Eyes. Compare to the robotic version, the Cyber Cyclops, and Eyepatch of Power.
Oh, wait, were you looking for That Guy With The Visor?
"The Purple People Eater" from the 1958 novelty song of the same name.
The trope namers are the original three cyclopes of Greek Classical Mythology: Arges, Steropes and Brontes. They were master craftsman and giants of considerable side and power (and prone to fits of rage); the Greeks coined the term "cyclopean" to refer to ancient, precusor structures that they presumed could only have been built by mighty giants. Their father Uranus was so afraid of their power and fits of rage that he imprisoned them in Tartarus. When their nephew Zeus finally freed them to help in overthrowing their brother Cronus, they worked together to forge Zeus' lightning bolt (each contributing one third of the weapon's elements; the blinding light, lethal heat, and deafening thunderclap, respectively). They also created Poseidon's trident and Hades' helmet of invinsibility. Eventually, the brothers were surpassed by Zeus' son, Hephaestus, to whom they and their descendents became assistants. They also created the solar and lunar bows and arrows of Apollo and Artemis.
Warhammer: Most one-eyed creatures have the ability to perceive the Winds of Magic. The Fimir are one-eyed, skull-faced amphibious creatures whose superior perception of the Winds of Magic allows them to roll six dice to channel instead of one, although they're too greedy to share the power dice produced by this channelling, and the Beastmen creature known as a Cygor - essentially a hybrid of a cyclops, a minotaur, and a giant - has a degree of magical perception that it uses to find, kill, and usually eat enemy spellcasters.
Another Cyclops, Gargarensis, is the main antagonist.
Cyclopes in Rift seem to be denizens of the Plane of Earth. They're built along the same large and solid lines as bahmi (although they tend to be even taller), but have ivory-yellow skin, vaguely bestial features, and the definitive single, centrally-positioned eye.
In Titan Quest, Polyphemus the Cyclops from the Odyssey appears as a boss. You also meet some other cyclops while ascending Mount Olympus.
Dragon's Dogma: Dark Arisen introduced the 'Gorecyclops', which are darker, evil versions of the normal cyclops.
On top of that, the 'Condemned Gorecyclops' was also introduced in Dark Arisen. This one is a gigantic enemy boss chained to a wall. It's one of the largest enemies in the game, and far larger than any other Cyclops.
Cyclopes are pretty common enemies in the Dragon Quest series.
Dark Souls has Kalameet, the one-eyed black dragon from the Artorias of the AbyssDLC.
Cyclopes are relatively tough enemies in Dark Souls II, and you can encounter one within the first minute of gameplay.
Big, blue cyclopes are boss monsters in Dragon's Crown, and you fight them two at a time.
The Eggplant Wizard from the Kid Icarus series is a cycloptic, purple wizard with the power to turn Pit into an eggplant. He's been in every Kid Icarus game to date, and also was a recurring villain on Captain N.
You can play against a team of cyclopes in the Sega Master System game Basketball Nightmare.
The strangely-named Unicorn Demon from Ghosts N Goblins is a somewhat traditional-looking cyclops.
The appropriately named Uniocs in Schlock Mercenary have one basketball-sized eye on top of a stalk on their shoulders above the mouth, their brains are apparently down in the pelvic area. Depth perception isn't a problem because their one big eye can rapidly shift focus and they can see on the microscopic scale as well. There's also a comic where it's mentioned that there was a Unioc dressed as a Cyclops at a physics convention.
One episode had him figure out this was detrimental to his plans because he lacked depth-perception. He spends the episode trying to grow a second eye through experiments, finally getting one via Spongebob's DNA...but Spongebob's naturally good personality begins to take over Plankton's and he ultimately has to get rid of it so he can continue his plans.
Loomis from The Smurfs Season 9 episode "The Smurf Odyssey".
Eyemore from the Biker Mice from Mars 2006 reboot episode "Manchurian Charley", who can hypnotize people with his one, massive eye.
Cyclopes aren't restricted to mythology — a number of defects in fetal development can result in birth of one-eyed creatures, although the severity of these defects and related disorders means these creatures usually die soon after. Exposure to natural or man-made poisons is often to blame nowadays.
Cy, the internet-famous one-eyed noseless kitten, who was born December 2005 and died a day later.
A one-eyed piglet with a severely deformed nose was also born in China in 2005.
Cyclopia, as it's known, can manifest in humans as well. You can Google it, but the pics can be rather squicky, so be warned. Most cyclopia babies don't survive.
The cyclopes from Greek legend are thought to have been based on a misconstrual of fossilized mammoth or other prehistoric elephant skulls. If there were no tusks present, the trunk hollow could easily be mistaken for a single eye socket (It's actually the nasal cavity). You'd even have tourist travel guides telling travelers where they could see a cyclops's remains.