Well, the wave form is just the visual representation of what's going on audio-wise. It shows the natural peaks and valleys of a sound. Obviously, there should be some differentiation there, which represents volume differences. Dynamics.
This is a nice wave. Notice the ups and downs? It "breathes."
The waves on the new Metallica album don't do this. They are a solid bar.
What happens as you do this, is the wave will get louder. In fact, the less dynamics (breathing, or ups and downs) in the wave, the closer to max loudness it gets. Problem is, there is only so loud you can make a basic waveform. (Comparatively. We always have a volume control on our audio equipment.) Once you have a solid bar, that's it. No more dynamics. Everything is as loud as everything else. That's basically compression, and in this case, taken to the max.
But Metallica went a bit further. They pushed the envelope so far, that they actually went past where you can. But just like those old amps pushed to their limits, they, and this album, begin to distort. What we term 'clipping.' If you listen to DM on a good stereo, especially headphones, not only does the total lack of dynamics show up, but you can actually hear certain loud sounds inducing this clipping - like Lars's snare hits, or the palm mutes of the guitars.