The most common misinterpretation of this theory is by people who seem to think of evolution as some kind of magical force, a tangible 'thing'. "Evolution goes slowly for a while, then speeds up, then goes slowly again... But if evolution is so scientific and all, how can it vary like this?"

Evolution is simpy a process. If one creature develops an improvement, this will allow the creature's species to wipe out other less developed species, to expand its habitat, etc. This dominant species will then evolve into several species over a sufficient period of time. (We're still talking big numbers here).*

You can then say that the average 'advancedness' of species on Earth has increased; evolution has 'sped up'. But this is a rather strange way of looking at it. Instead of punctuated equilibrium being a replacement to evolution, or an 'add-on', it is simply an explanation of what path evolution will take.

* Of course, the dominance of one species will not totally destroy all others. In fact, the pressures on the non-dominant species will cause natural selection on them to increase, so they will either evolve improvements of their own or die out.