I hate this.
I'm sure you already know about dynamic range compression. This is when during mixing, they dampen the sound waves with large amplitude, and then increase the volume of all the waves. This has the effect of making the entire song sound louder, at the expense of the aural fidelity of the music.
When I turn the volume down on "My Companjera," it sounds roughly the same volume as the other songs I'm listening to. However, those other songs still have more "space" left at the loud end of the range, so they have the opportunity to surprise me with, say, a relatively louder guitar part.
In some extreme cases, such as Metallica's Death Magnetic album (which is the poster child of the loudness war), the producer made it so loud that the sound waves exceeded the dynamic range of the medium, resulting in clipping (which sounds like distortion). Interestingly, Death Magnetic and Gogol Bordello's Transcontinental Hustle were both produced by Rick Rubin, which is not a coincidence.
I am no audiophile, but even I can appreciate the value of leaving the dynamic range intact. One of my favorite musicians, Steven Wilson, produced his own Porcupine Tree albums, as well as the excellent 2009 remasters of the early King Crimson albums. All of these albums sound quieter than most other albums in my collection, and I typically even turn the volume up a couple notches. The extra dynamics add a whole other dimension to these albums.
And finally, a note on format. A friend was asking me the other day if vinyl really does sound better than CDs. I responded with a very long-winded and overly technical way of saying "it depends," as a lot depends on your speakers, your record player, your cartridge, your stylus, etc. However, there is one advantage inherent to vinyl (which I didn't consider at the time of that conversation), which is an actual limitation to the most common digital formats: vinyl has no limitation on dynamic range at the lower end. If the bumps within the grooves are smaller, the volume is lower. That's all there is to it. (There is a limitation at the upper end, as bumps too large can cause the needle to jump out of the groove, though this could be abated somewhat by altering the setup.)
Case in point: While listening to The Flaming Lips' Transmissions From The Satellite Heart, I was simultaneously recording it into a .wav file. I believe it was the track "Plastic Jesus" where I could clearly hear soft vocals coming out of my stereo; when I played it back on the computer, however, I could not hear much of anything, and my mp3s of this track are nothing more than a few incoherent noises barely audible over the background static from the headphones. It is, of course, possible for me to amplify the audio input as it is recorded, but this is tantamount to reducing the dynamic range.
This is what makes it such a pleasure to listen to my Carl Orff Carmina Burana vinyl. The loud parts are loud, and even thunderous, and the quiet parts are soft and serene. If I transferred this recording to a digital format, I'm not sure I'd even be able to hear half of it.
To summarize, I love dynamics. I don't remember if someone else said this, or if I made it up by myself, but good music is defined not by the noise, but by the silence. I can't wait for the loudness war to end.