As you know, Robert, this chart has two axes: the horizontal one refers to positions in the mouth and vocal tract; the vertical to the various ways that air can be stopped or constricted to make sounds. Plosives, for example, which involve air being completely stopped and then released, can be made at various points in the mouth from the lips to the epiglottis, but the lips can also be used to make other kinds of sound (nasals, trills, etc.).
The shaded parts on the map represent "impossible" sounds - impossible because of the limitations of human anatomy. A sound that requires vibrating a loose flap of skin, for example, can't be made using a part of the mouth that has no such feature.
But it's the empty-yet-unshaded parts that are most interesting. These represent sounds that are physically possible but that have not yet been discovered in any known language. I suppose an obvious comparison is with gaps in the periodic table deliberately left by Mendeleev for others to fill after him. What could be more enticing? Who wouldn't want to be the person to find that element and get to name it? Who wouldn't want to be the first to identify a particular phonetic sound and add it to the IPA map?
I'm reminded also of the white spaces left in nineteenth-century maps of Africa: an enticement to young explorers to go off and 'discover' and name new countries. This isn't entirely coincidental. Some seekers after rare minerals must have been among those who donned pith helmets to go into the Amazonian or African jungles. Seekers after rare phonemes go there now. White space is catnip to imperialists, whatever their brand of imperialism.