Punctuated Equilibrium is a theory about how the evolutionary process works and it describes how species originate rapidly. Shortly described, punctuated equilibrium can be represented by a group of organisms that get isolated from the rest of their species. They evolve fast, because they are a small group and then they can spread and replace their parent species. So, evolution happened in rapid bursts over short periods, according to punctuated equilibrium theory.
Fossil records are very static, show lack of change and the lack of transitional forms. So, the sudden appearance of new organisms in sedimentary layers is used to support punctuated equilibrium theory.