There are two situations being covered in that explanation, which is probably part of what is causing the confusion.
Prefocusing simply means that you set the focus before you actually take the photo. This can be useful for a number of reasons, including needing faster shutter response (the photo takes quicker after you press the shutter) or needing to focus on something other than where the focal point will be in the shot.
In the first case, auto-focus normally takes some time to figure out where it needs to focus. When you push the shutter release, the camera must focus, make exposure adjustments, and only then can it take the photo. This processing can result in a significant delay ranging anywhere from a few dozen to a few hundred milliseconds or more. If you are shooting something where you need a responsive shutter (action shots for example) that extra time to focus may make you miss your shot. By pre-focusing on something at the distance you want to focus on for the photo, you can avoid the delay of waiting for the focus to process.
For the second case, you may be shooting at something where the focus point either ends up on a point that is not at the right distance or is not something the camera can easily focus on (low contrast regions) when you have the shot composed the way you want. In this case, known as focus and recompose, pre-focus allows you to focus on a more ideal area at the distance you want to shoot and get the focus point set. After that, you can turn the camera to compose the shot the way you wanted and then take the photo. Note that it is important not to move the camera closer or further away from your subject when doing this or the pre-focus won't be correct. Also, if you change the angle significantly you may still end up with some error in your focus due to the way the image plane for the focal length is made, though this is normally only a problem for major recomposes or a really shallow depth of field.