Over Excursion or Clipping...

You dont want to get to the point where you hear clipping. Bad...very bad. Over excursion can happen well below clipping. Clipping involves mainly amp output limitations where as over excursion can happen any time. Its more dependent on speaker limitations than amp limitations.

When your amp is clipping, your music will generally sound compressed and quite distorted. As far as over-excursion, I've overdone that to the point (long ago) that the speaker cone bottomed out and made a loud 'thwack!'.

I experienced the former with too little power and the latter with too much power (or rather, poor judgment using a lot).

It sounds loud even if it really isn't - because of all the distortion.