The oft-cited answer to this sort of question is that they came from fossils skulls of mammoths or some type of elephant, because there is, of course, a singular large opening in the front for the nasal passage. Although the chance discovery of this sort of fossil could have reinforced a belief in a Cyclopes there is no evidence that it reinforced, caused, or influenced this tradition. It may have occurred, but that is pure speculation.

To understand the legend that appears in The Odyssey, we need to understand that there is a core, widespread legend behind the piece of literature. The legend, which manifests from Scandinavia to Greece involves a powerful supernatural being that is interacting with a man, the hero of the legend. The man cleverly tells the supernatural being that his name is either "nobody" or "self." The hero either pokes out one of the eyes of his adversary or he flicks a burning ember into the creature's eye. This gives him the chance to flee from the injured entity who screams in pain. The creature's relatives ask what happened and he responds either that nobody or self has hurt me, to which the hero hears a response, "well if you hurt yourself, then you have yourself to blame" - or something along that line.

The supernatural being is not normally a Cyclopes, but it is easy to imagine how a creature that ends the legend with one eye, could just as easily begin the legend that way, and end completely blinded. While this too is speculation, I suspect that what we see in The Odyssey is a misunderstanding of the legend or a clever literary manipulation of the legend to arrive at the device as it appears in that piece of literature. But that can be little more than speculation.

The important thing to understand about this large group of legends is that the story from The Odyssey is a manifestation of a widespread legend, and although in literature it follows its own unique pattern, the supernatural adversary was well known in European folklore. That creature assumed many forms, but it folded into a large tradition. The Cyclopes didn't go anywhere, he assumed various other forms and lived on.