Rendering is the hard work that all computers do when changing the video time line into a rendered video, ready for the web, or to burn onto a DVD.

Video rendering takes up serious computer memory real estate. Computers that are being demanded too much of simply crash. Thus the above article.

Pre rendering specific places on the timeline on their own before rendering the rest of the video allows the computer to finish one difficult, memory hungry task without working on anything else. In Premiere CS Series, this is accomplished by narrowing down the chosen portion of time line one wishes to render.

The pre render is different from final rendering. The pre render prepares the time line for the final render.

Hope that helps.