Compressors and limiters (very fast acting compressors) are required so that music can be comfortably transposed or carried by the medium. They reduce the musical peaks and raise the low level signals. For instance, on vinyl records if the music is recorded too softly it can be overwhelmed by the noise floor. If too loud, playback time per side is greatly reduced and the stylus may literally pop out of the groove. FM radio and reel to reel tape also have dynamic range limitations that virtually mandated the use of dynamic compression in order to fit the music within the medium.
With modern digital recording and playback equipment there's no technical reason to use compressors or limiters. However, in pop/rock recordings there are any number of artistic reasons to use compressors. Bonham's classic drum sound or Santana's mid-to recent period guitar tone are dependent upon compressors.
To address Saki70's question: some music just doesn't sound right without compression. Rock without compression doesn't sound like rock and roll. Do you really want to take the crunch out of the guitars?
One of the tell tale signs of an untrained musician is their wildly fluctuating dynamics. Such dynamics are also considered a sign of poor recording engineering. In a single recording the music shouldn't be so soft that you turn the volume up and then later have to turn the volume down because it's now too loud.
Compressors and limiters I'm referring to are conceptually different than and have nothing to do with data compressors such as MP4.
