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Basically, the more you compress sound, the more subtleties are lost. Sound is a wave, and the further you compress a sound wave, the "chunkier" the wave gets. Instead of a smooth line, imagine it as a series of rectangular bars that try to approximate the curve (the poster describes it better than I could).

This has been a problem for years. The more acoustic the recorded medium, the more of the wave is preserved. So records are less compressed than CDs, for example, though CDs still retain most of the quality. As audio equipment has improved, you can hear the flaws in an old recording, but if you listen to a record on a record player, the nuances can be incredible.

As the 90s went on, sound engineers began compressing the sound more to boost the volume. Imagine a horizontal line on a piece of paper. The sound wave would be say, a third up on the paper. To boost the volume, the wave ends up covering say 2/3 of the paper, even the entire paper. The wave itself becomes less detailed as a result.

The digitalization of music is a huge problem in terms of sound quality. Like the article says, when sound waves have to be translated as 1s and 0s, the wave becomes even more "chunky", and a ton of quality is lost. It gives the music a kind of unrealistic quality that's subtle, you might not notice it offhand.

It's an interesting problem and a real one - check out the article for more details.