Paleontological term, coined by Stephen Jay Gould, to describe the uneven progression of evolution. Instead of being a continuous, gradual process, evolution is characterized by very short periods of extreme diversification and growth interspersed between long periods of slow change. This idea is based on evidence in the fossil record where strata for many ages contain the same organisms. Abruptly, within a short geological period of time, a whole new set of organisms are found. The theory is based on the idea that periods of intense growth are initiated by a novel adaptation which gives a particular species an amazing advantage over its environment. All interacting species are quickly selected for those that can adapt to this new change. Other causes of puctuated equilibrium can be quick environmental changes such as a meteor or ice-age.

An example would be the Cambrian explosion, if I remember correctly, where the evolution of tissues that can form hard structures (i.e. teeth and body armor) resulted in an astounding amount of growth in a short period of time as predator and prey counter-evolved to outdo each other with these new weapons and defense systems. The trilobites are a prime example of this with their hard chitinous bodies. The large soft bodied organisms of the Precambrian Era all but disappeared during this prolific diversification.

The reason I thought of this topic, I must sheepishly admit, is from watching the movie version of X-men where they say in the introduction that evolution is a slow and gradual process, but every now and then, it proceeds very rapidly - hence the sudden emergence of mutants within the human population. Although the selective pressure for mutants isn't obvious, its a fun idea. There are certainly worse perversions of science in the movies (e.g. the new version of Godzilla)