Realism is the claim that the world out there is pretty much as it seems to be. If that sounds vague, there is a reason for it - realism can be taken in a variety of different ways. Naive realism is the position that the world out there is pretty much as it appears at a very specific, low level. If I see something that looks like a red apple, that conscious event corresponds to an actual red apple in the real world. The apple appears red to me because it really is red, period. The apple reflects photons of red light, and they get absorbed by my retinas, and my brain faithfully registers the information that there is a red apple in front of me. Naive realism takes the mind to be merely reflecting the reality out there.
Naive realism is not true, however, because of course there are no red photons. That is, while things seem red to us, all that really strikes the retinas in the backs of our eyes are photons of certain wavelengths. These wavelengths are just numbers representing a particular periodicity that the photons display. There is nothing in those numbers that suggests redness as we experience it. The association between wavelengths of light in a certain range and redness is one our minds make up out of whole cloth. Color is just the mind's way of representing different wavelengths of light, but we could have evolved to use some completely different representation with no loss of information about the real world.
Consider the inverted spectrum argument. If someone were born with their optic nerves cross-wired in such a way that when they were shown red it looked green to them and vice versa; so that in effect their perceived color wheel were rotated by 180 degrees, they might never know it. They would receive the same information about the world, and they would learn the color names as a small child, and they would agree that a sunset is a deep orange, but it would not really look orange to them the way it does to you. It would look teal, but they would call it "orange".
The inverted spectrum argument is usually made to convince people of the distinction between cognitive information and ineffable qualia: my inverted spectrum twin has the same information about the world that I do, but entirely different qualia. I am using the scenario to make a different point, however. It should be clear that, given me and my inverted spectrum twin, there is no fact of the matter of which of us is seeing the "right" view of the world. There are photons, there are perceived hues in the mind, and there is a correspondence between the two. The question of what is the "correct" correspondence between the two just doesn't make sense. Color as perceived serves as a very good carrier of information that comes into our bodies by way of photons striking the retina, but one could speculate on other ways. Perhaps some alien species could consciously discriminate between all the wavelengths of color that we do, but perceive them through some sort of tactile radar-sense, or some other sense modality we can not even imagine.
Similarly, while the sensation of redness conveys certain information to us in our visual field, that same sensation could conceivably convey different information. Perhaps our sense of smell could be wired into some perceptual field of color, for example.
If there are no red photons, and color exists only in our minds, what about sounds? By a similar argument, there is no middle C "out there" as it sounds to us in our mind's ear. There are just periodic pulses of fluid pressure. Hot and cold are just the aggregate motion of huge numbers of molecules and similarly could conceivably be represented in our minds with completely different qualia. The same could be said of pressure against skin, smell, and taste. Our qualia are only in our minds, and they are created there.
So at this low level of the qualitative sensory aspects of our world, naive realism is false. Assuming that we can claim to know something about the real world, that the world as we experience it internally is in some way like the world out there, at what level of abstraction does realism start to become true?
I would like to suggest that realism is false at a higher level of abstraction than we generally assume. That is, more of the things we think we perceive about the world are created in our minds than we acknowledge. The real world (almost certainly) exists, and its reality constrains what we perceive, but does not determine it. Most of the structures, patterns, and dynamics of the world are "really" out there and exhibit a lot of the regularities we think they do in the same sense that photons of certain wavelengths are really out there. But as with redness, the ways in which we experience them are not really out there. Things are abstractions. We create all things, we infer unity and mid-level individuation in the world. Seen in this light, consciousness has a much bigger job than just painting the apple red. It must create reality much more broadly, including the apple itself. Just as there are no red photons, there are no rocks, cars, dogs, or numbers. Nature presents us with a wash of particles, a continuous flux of quantum stuff, and we overlay this flux with stories about cars and rocks.