Atlantis is first mentioned by Plato, in the works Timaeus and Critias. From Timeaus:
This power came forth out of the Atlantic Ocean, for in those days the Atlantic was navigable; and there was an island situated in front of the straits which are by you called the Pillars of Heracles; the island was larger than Libya and Asia put together, and was the way to other islands, and from these you might pass to the whole of the opposite continent which surrounded the true ocean; for this sea which is within the Straits of Heracles is only a harbour, having a narrow entrance, but that other is a real sea, and the surrounding land may be most truly called a boundless continent. Now in this island of Atlantis there was a great and wonderful empire which had rule over the whole island and several others, and over parts of the continent, and, furthermore, the men of Atlantis had subjected the parts of Libya within the columns of Heracles as far as Egypt, and of Europe as far as Tyrrhenia.And from Critias:
There were many special laws affecting the several kings inscribed about the temples, but the most important was the following: They were not to take up arms against one another, and they were all to come to the rescue if any one in any of their cities attempted to overthrow the royal house; like their ancestors, they were to deliberate in common about war and other matters, giving the supremacy to the descendants of Atlas. And the king was not to have the power of life and death over any of his kinsmen unless he had the assent of the majority of the ten.The ideas contained in that last paragraph are interesting to me. Plato was trying to layer his philosopher-kings over a 'real' place, or at least a place that was thought of to be real. The ideals espoused here seem familiar: Limitations on kingly power, cooperation among disparate groups to support the central government. Sort of a federation, across the Atlantic from Greece...
Another interesting tidbit about Atlantis is that none of Plato's contemporaries, or even those who followed after him, mention Atlantis, unless in reference to what Plato himself wrote. Plato appears to be the sole source of stories about the mysterious sinking island.
However, it's an idea that has stuck, and been used as a meme canvas to elaborate and speculate and elucidate the ideas of various philosophers. It's been used as an argument against the era of sterile rationality and scientific inquiry that removes the art, wonder, and blank spaces on the map. It's a favorite of those with fringe theories: ufologists, racists, geological mavericks, historical researchers, fantastic writers for the pulps and television, and even rock stars. I'm sure I'll be looking into it a bit more as time goes on.