"Qualia" is effectively a name for all those properties which constitute your experience of the world, but which do not exist in the current ontology of natural science (thus we have the spectacle of people on this site needing to talk about "how it feels" to be a brain or a computer program, an additional property instinctively tacked on to the physical description precisely to make up for this lack).

This is a problem that has been building in scientific culture for centuries, ever since a distinction between primary and secondary properties was introduced. Mathematical physics raised the description and analysis of the "primary" properties - space, quantity, causality - to a high art, while the "secondary" properties - all of sensation, to begin with, apart from the bare geometric form of things - were put to one side. And there have always been a few people so enraptured by the power of physics and related disciplines that they were prepared to simply deny the existence of the ontological remainder (just as there have been "irrationalists" who were really engaged in affirming the reality of what was being denied).

We are now at the stage of figuring out rather detailed correlations between parts and states of the brain, described in material terms, and aspects of conscious experience, as experienced and reported "subjectively" or "in the first person". But a correlation is not yet an identity (and the verifiable correlations are still mostly of the form "X has something to do with Y"). Mostly people are being property dualists without realizing it: they believe their experiences are real, they believe those experiences are identical with brain states, but out of sheer habit they haven't noticed that the two sides of the identity are actually quite different ontologically.

Dennett belongs to that minority of materialists, more logically consistent but also more in denial of reality, who really are trying to deny the existence of the secondary properties, now known as qualia. It's possible to read him otherwise, because he does talk about his own experience; but if you look at his checklist of properties to deny, you can see he's a sort of neo-behaviorist, focused on verbal behavior. Indeed, the only thing neo about his behaviorism is that he has a physical model of how this behavior is caused (connectionist neural networks). But he is careful to say quite explicitly that there is no "Cartesian theater", no phenomenal color, no inner life, just people talking about these things.

I cannot tell if you are truly in Dennett's camp, or if you're just rejecting the view that there's something especially problematic about explaining sensations. A lot of people who talk about qualia are trying to emphasize that a description of human beings in terms of causal interactions between pieces of matter is leaving something out. But the things being left out are not in any way elusive or ineffable.

Science seems to be telling us that your whole life, everything you have ever experienced, is nothing but changes of state occurring in a few trillion neurons which have been sitting inside the same small dark space (your skull) for a few decades. Now if that's the case, I may not be able to write an equation describing the dynamics, but I do know what that is physically. It's a large number of electrons and quarks suspended in space by electromagnetic fields. If we are to unconditionally accept this as a description of what our lives and experiences really are, then we have to be able to identify everything - everything - we have ever thought, known, or done, the whole of our subjective realities, as a process composed of nothing but changes of states of particles all occurring within a few cubic centimeters of space. And I have no hesitation at all in saying that this is impossible, at least if the basic ingredients, those particles and fields, are understood as we currently conceive them to be.

Quite apart from the peculiar difficulty involved in identifying complex subjective states like "going diving in the Caribbean on your 25th birthday" with the electrical state of a captive neuronal porridge, the basic raw ingredients of subjective experience, like color qualia, simply aren't there in an arrangement of pointlike objects in space. This is why materialists who aren't eliminativists like Dennett are instead dualists, whether they realize it or not - because they simultaneously assert the existence of both the world of atoms in space and the world of subjective experience. These two worlds may be correlated, that is being demonstrated every day by neuroscience, but they simply cannot be identified under the physical ontology we have.

In my opinion the future lies with a new monism. But "physics" will have to be reconceptualized, if that world of subjective experience really is going to be found somewhere inside the skull, because as things stand there is nothing like it in there. I would also say that doing this is going to require a leap as big as anything in human intellectual and cultural history. It won't just be a matter of identifying the "neural correlate of consciousness". Someone is going to have to go right back to the epistemic beginning, before the distinction between primary and secondary properties, and rethink the whole of natural science from Galileo through to molecular neuroscience, while keeping the secondary properties in view. You can always reduce science to subjectivity, if you're prepared to let go of your models and remember that everything that has ever happened to you has occurred within your own subjective experience, so that's the easy part. What we're aiming for is far more difficult, namely, an objective world-picture which really does contain subjective experience and is true to its nature while also encompassing everything else. Of course, all those people who are out there trying to "naturalize subjective experience" or "naturalize phenomenology" are trying to do this, but without exception they presuppose the current "naturalistic" ontology, and yet somehow that is where the change and the progress has to occur.