David Chalmers did not express it clearly in that quote (which is a loaded question, btw). What he meant to ask is "What Mary learned when she saw the red color for the first time?"
As the story goes, Mary is a brilliant scientist and a leading expert in everything color -- what they are (bands in EM spectrum), how they're sensed by the eyes, and how they reconstructed by the brain. Amazingly she accomplished all that w/o actually seeing a color. She is not colorblind, but she has been living in a black and white environment. Her lab, home, furniture, screens all monochrome, the shades of gray... until one day when she got out and saw red leaves on the trees (it was a beautiful day in the fall).
And that was Chalmers's question -- what Mary had learned in that moment? She already knew everything there is to know about colors. Yet, seeing red was not just a novel experience, it enriched her life in the most profound way -- which would not be possible unless she had learned something just from seeing the color... but what exactly did she learn? <== and that, again, is the so-called "hard problem".
A (very short) Answer
Now if you think about it, the "hard problem" question is essentially about the nature of fundamental concepts -- also platonic forms, also John Locke's "simple ideas", also Immanuel Kant's "intuitions", etc... like your concept of a "chair", or a "jump", or, indeed, of what counts as "red".
It is a knowledge of sorts -- like, you know what a chair is, don't you? But try and give a precise definition of what is -- and what isn't! -- a chair in rational terms, and you will soon find yourself grasping for words and only becoming more frustrated, realizing... wait, you don't know what a freaking chair is!?..
Well, strictly speaking, you don't, for it is not a rational knowledge.1 What you do have, instead, is a pretty good idea of what constitutes a chair. And, unlike knowledge, ideas/concepts are not products of your rational Self. They are created by your neural network AI, commonly referred to as your "subconsciousness".2
In fact, "getting ideas" of things is what neutral networks do as their way of processing experiences. Being, at its core, an image recognition system, a neural net treats everything as a picture,3 looking for similar patterns and anti-patterns in different depictions of the same class/type of things.
A concept of a chair, therefore, is but a collection of numerous patterns found in things classified as chairs by some trusted authority. Plus the anti-patterns, their presence strongly suggesting the thing is not a chair.
And that's your qualia, hopelessly subjective, as it should be, a sea of simple concepts. The rational Self then uses them as lego pieces to assemble mental models, each explaining a particular aspect of reality -- and if true, it's knowledge. The individual models, in turn, become pieces of the ultimate jigsaw puzzle, the Big Picture -- a complete simulation of the world. Modeling ourselves, as a part of it, makes us self-aware and, thus, capable of conscious choice.
And... that's all there is to it. The real hard problem is not the consciousness -- it's us, creating obstacles upon obstacles, making something that everyone should have pretty much out of reach.
1 We can call it "irrational knowledge", but I'm afraid that would bread a lot of confusion.
2 In some way, it functions very similarly to a Flight Computer, first adopted in the modern fighter jets (F-16 was the first to take full advantage). At the time, they wanted to make them extremely agile, but that would also make them aerodynamically unstable, impossible for a human to control. Enter Flight Computer. Capable of making minute adjustments of individual control surfaces every split second, and could fly a brick with winglets (and so it did with Space Shuttle). The human pilot is still there, of course, but they can only access FC. The good FC then makes the pilot feel like they are in control, by doing its best to interpret and accommodate the pilot's intentions. Or not, if the FC knows better, as it happened with US Airways Flight 1549 (the "Miracle on the Hudson"), when, for the last minute of the fight, the FC diligently ignored the pilot's trying to lift the plane nose up, which would have ended in a stall like this...
3 the actual meaning of "being superficial"