The dictionary defines the word paradox as a statement or proposition that, despite sound reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory.
Such is the nature of audio transparency. Invisible sound.
A seeming paradox.
On the one hand, we can never hope to see sound. So the idea that some sound appears cluttered or opaque is certainly a contradiction.
On the other hand, the whole premise of a sonic image is based on visual metaphors. We have few choices of words when it comes to describing that which we hear.
Transparent sound occurs when the sonic clutter between instruments and voices disappears. The first time you hear a lack of clutter in the music the meaning of transparent sound will be obvious.
How to get there? Mostly through electronics: lower jitter levels, less feedback, greater linearity—though lower distortion and lower mass speaker drivers can help as well.
Is it something we can measure? Not directly. And worse, just because you have some of the key elements of design in place doesn’t mean it gets more transparent.
As in anything it’s a matter of optimizing the entire chain.