I've found its difficult to tell the difference at low volumes where there is no clipping or compression. At moderate volumes with music containing a mix of quiet and loud passages you can hear the onset of compression and distortion. It manifests itself as loose one note bass, smeared drums and shrill, unclear music. Switching to a better amp, usually a more powerful amp, means you can play the speakers much more loudly without the nasty artifacts you get from a clipping amp trying to reproduce quick musical transients.
There is a great jazz cover of "Walking on the Moon" by The Yuri Honing Trio that has excellent drum and sax attack and quiet plucking that make it ideal for testing your system. Bass, drums and sax go from barely audible to not hearing yourself speak and back again several times. You'll know if your amp clips or how well your speakers perform with this one.
When my brother visits he brings his favourite CDs and DVDs and keeps raising the volume to much higher levels than I am used to and complains my system doesn't sound loud enough.
He is used to hearing much more distortion from clipping on his system at lower volumes.
