He says for example (camera on Manual) "set your lens to f/5.6, place subject up against house... look through viewfinder and focus on subject. Adjust your shutter speed until the camera's light meter indicates a "correct" exposure in your viewfinder and take the photograph".
This is typical of the book's vague and unhelpful style. Personally I dislike the book intensely, but for some reason, many people seem to love it. Anyway, the important thing to understand is that your camera's built in meter (already explained by others) is assuming that the scene/subject that you are metering should average out to a a "middle" grey level of brightness. For an "average" scene it may be true that "middle" grey is a good balance to aim for.
However, every scene does not always average out to middle grey. Think of a snow scene, or a night scene, or something in a dark forest, etc.. Also, you have the option of different metering modes, which meter more or less of the subject/scene (spot, partial, centre weighted average and evaluative in Canon speak - Nikon will have similar options but perhaps with different terminology) so you need to decide what metering mode is best and also how to interpret the brightness of the part of the subject/scene that you are metering. To keep things simple for now, let's stick with evaluative (I think it's called matrix metering in the Nikon system).....
Following Peterson's example above, of a person against the side of a house, what colour/tone/shade is the house - is it red brick, painted white, perhaps dark stained wood, or maybe grey concrete? The camera certainly won't have a clue what colour/tone it should be. All it can use as a guideline for interpretation is that overall the scene should average out to middle grey - the safe bet. That might work fairly well if the house os finished in brick or concrete, but what if it is painted white? The expanse of white will fool the camera (and its meter) which will try to lower the exposure to turn the white into middle grey. If you are shooting with manual exposure and use the meter needle to guide you then, if you centre the needle, you will be accomplishing the same thing that the camera would on auto by aiming to get the scene to be middle grey.
If the house was very dark then the same thing would happen in reverse. Left on auto the camera would increase the exposure to brighten it up to middle grey. If you shoot in manual and aim for a centred needle then you too will be aiming for an image that looks middle brightness, rather than capturing the true darkness of the house.
The problem is compounded if you adjust your composition, by zooming with the lens or with your feet to include more or less of the house in the picture. Suppose your subject is a groom, in a black tuxedo, against a dark building. The only paler elements of the scene will be his skin and his shirt and tie. If you follow the instructions to adjust the exposure until the meter indicates a "correct" exposure, where should the meter needle be? I can tell you now that it will not be in the middle! If you do set the needle in the middle then the scene will be overexposed and your groom's face will be bleached to pure white. If you were to add the bride to the scene, and still keep a lot of the building as part of the image then her dress would also be blown out and lose all detail and shape.
One big weakness of the book is that he uses these glib, casual phrases, like "correct exposure", but does not give you any clue to understand what that really means in terms of positioning the meter needle or dialing in some Exposure Compensation when shooting in one of the autoexposure modes. He also completely fails to advise use of the histogram on the camera to check that your exposure is indeed correct. It is not sufficient to look at the image and make conclusions about the accuracy of your exposure from that. The histogram is what you need to check.
Bottom line - camera meters are really stupid. They do not know what you are pointing them at or how bright that thing should be. You have to guide the camera, or interpret the meter and set the exposure accordingly. Darker scenes should show an exposure below the zero mark while brighter scenes should show an exposure above the zero mark. Just how much depends on the exact makeup of the scene and which metering technique you choose to use. With skill and experience those judgements become easier to make, but with digital photography and the ready availability of the histogram it is easy enough to check your results and adjust and try again if you need to.
Sorry to waffle on.
Here's some more reading....
http://www.luminous-landscape.com/tutorials/understanding-series/understandexposure.shtml
http://www.apogeephoto.com/march2005/jaltengarten32005.shtml
http://www.cambridgeincolour.com/tutorials/camera-metering.htm
http://www.cambridgeincolour.com/tutorials/histograms1.htm
http://daystarvisions.com/Docs/Tuts/Meter/pg1.html
http://www.photozone.de/Technique
http://ronbigelow.com/articles/histograms-1/histograms-1.htm
http://www.michaelthementor.com/lessons.cfm?lessonID=28
