The "discarded image" refers to the Medieval model of the universe, and how intellectually satisfying it is -- not in the sense that we can still believe it to be correct (it was a geocentric model, after all), but in the sense that they conceived the universe as intricately organized, with "a place for everything and everything in its place." To this end, Lewis is constantly correcting common misperceptions about what the Medieval model actually was.
One of the myths that Lewis debunks is that the medievals thought the earth is flat. Lewis refutes this rather easily by simply quoting and referencing some of the myriad of statements in the ancient world as well as the early and late Middle Ages that the earth is round. If you want to do some more research on this, I recommend Inventing the Flat Earth: Columbus and Modern Historians by Jeffrey Burton Russell, a historian at the University of California at Santa Barbara. To put it simply, every educated person from the third century BC onwards knew that the earth is round, and most of the uneducated ones did too.
Another belief that is commonly ascribed to the medievals is that they thought the universe was small. There is a half-truth here: they certainly believed the universe to be orders of magnitude smaller than what modern science has revealed. But as Lewis repeatedly points out, they still thought it was unimaginably large. He writes,
the fact that the height of the stars in the medieval astronomy is very small compared with their distance in the modern, will turn out not to have the kind of importance you anticipated. For thought and imagination, ten million miles and a thousand million are much the same. Both can be conceived (that is, we can do sums with both) and neither can be imagined; and the more imagination we have the better we shall know this.
A third distortion that Lewis addresses is that, by placing the earth at the center of the universe, they were attributing to it a position of privilege or significance. Actually, precisely the opposite is the case: the center of the universe was the least privileged and the least significant place therein. That's why they also placed hell in the center of the earth, and Satan at the center of hell. The reason the physical center is the least prestigious place in the universe is
Because, as Dante was to say more clearly than anyone else, the spatial order is the opposite of the spiritual, and the material cosmos mirrors, hence reverses, the reality, so that what is truly the rim seems to us the hub... We watch ‘the spectacle of the celestial dance’ from its outskirts. Our highest privilege is to imitate it in such measure as we can. The medieval Model is, if we may use the word, anthropo-peripheral. We are creatures of the Margin.
Again, this is something that can easily be verified by reading the medieval writers. The earth wasn't so much at the center of the universe as it was at the bottom of the universe.
Lewis devotes the Epilogue of The Discarded Image to a fourth, and the most controversial, point; an issue he had addressed before in "The Funeral of a Great Myth" in Christian Reflections and to a lesser extent in "Is Theology Poetry?" in The Weight of Glory and Other Addresses. The issue in question is the popular conception of evolution, that life -- and by extension the entire universe -- is slowly improving. Lewis makes a sharp distinction between this popular conception and the actual theory of evolution as held by scientists, which is about change rather than improvement. I want to make this as clear as possible: Lewis takes it for granted that evolution has occurred, as he makes abundantly clear in "Funeral of a Great Myth". What he challenges is the popular view.
His point of challenge is the idea that scientific evidence slowly showed the medieval model to be incorrect, and that we were led to replace it with the evolutionary model because of the scientific evidence. Lewis argues to the contrary that poetry, music, and literature in the 1700s and 1800s advocated for and glorified the evolutionary model, long before there was any scientific evidence for it. For example, The Ring of the Nibelung, the four-opera cycle by Wagner, which was well underway by the time Darwin published The Origin of Species, was based on this concept. Lewis's point is that we were not led to accept evolution solely by the scientific evidence. The idea of progress or improvement had already permeated itself into the imagination and habitual thinking patterns of Western culture, and it was only then that scientific evidence came along to confirm it (although, again, the scientific evidence doesn't confirm the popular view).
Again, I want to reiterate that Lewis accepted evolution. What he is challenging is that it was originally conceived and accepted in a purely scientific atmosphere, where the desire for it to be true played no role. As such, it is invalid to look down upon the medievals for not proportioning their belief to the evidence when we don't do it either.
(reposted from OregonLive and the American Scientific Affiliation)