After reading Consciousness Explained a number of times, my understanding of what red is is this: "red" is a shorthand term we use for a property that certain objects have of causing certain responses in the perceptual systems of certain creatures. The reason we have to use a shorthand term for the property is that the property "red" does not map to any simple physical or chemical property of the objects which are red (i.e., we can't say that an object is red if and only if it reflects light of a certain wavelength, for example); in physical or chemical terms, the set of things which are red is a horribly gerrymandered set of objects with no obvious rhyme or reason to it--other than the fact that they all look red to normally sighted humans. So basically "red" is the property of looking red to normally sighted humans (or other creatures that see the color red).
This may seem circular ("red things are things that look red"), but it really isn't. We could, if we really wanted to, write down in detail exactly how objects that are red produce the appropriate responses in creatures that see red--we could trace out in detail the effects of photons impinging on retinas, sending nerve signals into the visual areas of brains, having those signals integrated with the overall perceptual system of the brain in question, eventually ending up with outputs like "I see a red thing over there." So if we really wanted to, we could work out a definition of "red" in terms of actual physical and chemical properties of objects, along with the properties of the eyes and brains that perceive them. This would replace the "look red" part of the apparently circular definition above with a horrendously complicated explanation of why red things look red--but that wouldn't ultimately add anything to the concept. We would still end up saying the same thing, just in a much more long-winded way.
So far I have only discussed "red" in terms of objects which are red; but there is also the problem (at least to some people it's a problem) of defining the "red" that exists in the mind of a creature that is perceiving a red object. My definition of this "red" is just a mirror image of my definition above of the other "red": the "red" that exists in your mind is just a shorthand term for the mental state in you that is "activated" (I know I'm hand-waving a bit here) when you perceive a red object. This problem usually arises when people ask things like "What's the difference between red and green?" Or, as Jonathan asks, "What's the difference between red and sweet?" Why is red "red" and sweet "sweet" and not the other way around? To me (and I think to Dennett, based on my reading of his book) all these questions are (no offense to anyone) simply misguided. Red is "red" simply because that is what it is like to perceive a red object. There is something in your brain state that is different when you perceive red than when you perceive sweet, and that is why red is red and sweet is sweet. There isn't any more to it than that.
I found the discussion of this topic in the book particularly interesting because I am partially red-green colorblind; there are some shades of red and green that look exactly the same to me (there are others that I can distinguish, luckily including such things as traffic lights and stop signs, so I don't have trouble driving!). When I found out that I was partly colorblind, as a child, I used to spend a lot of time wondering whether things that looked red to me looked the same to other people--even if I could use the same word, "red", to describe, say, a given traffic light, I wondered whether that traffic light looked the same to me as it looked to someone with normal color vision. How could I be sure that I was correctly labeling all my inner mental states, if my visual system was known to work differently? The answer that Dennett would give (and which I myself would give) is that probably my inner mental states that I label with the word "red" are different from other people's--but who cares? As long as I stop my car at the same traffic light as everybody else, then the light is indeed red for me in the only sense that really matters.