A5 for instance

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Note added at 8 mins (2006-05-16 09:55:34 GMT)
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The A series of formats was conceived so that the letter A followed by an integer represents a certain size of a piece of paper. Thus A4 measures 210 x 297mm. Atarting with A0 ("ay nought"), each increasing integer represents a halving of size on the previous index. Thus A5 (reasonably close to the usual paperback book size) is 210 x 149mm. The reduction is along the diagonal of the rectangle.

A-format paper stock replaced previous formats such as Foolscap, Legal, et c., some 30 and more years ago.

For print production reasons, printed matter very rarely follows A-format paper stock sizes. This is because certain printers' marks (index marks, colour separation marks, trim markers) have to be mechanically trimmed after printing and before binding.

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Note added at 14 mins (2006-05-16 10:01:43 GMT)
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Regarding other book and magazine formats, there is an endless number of them, each designer choosing one to suit.

Leaflets and ring-bound reports, et c., are most often printed on A-formated paper which is sheet-fed into the printing and folding machines, and then possibly into binding machines.

Books and other bound printed matter is generally printed on non-A-format paper which comes from a roll and is "web-fed" into the printing and binding machines. After that, it goes on to be fed into a trimmer and folder so the ultimate result is a book(let).

Measure a few magazines and books around you, and you will see that each is different. The precise trim size is determined by the designer who bears in mind the quoted tolerances of the machinery involved, _inter alia_.

If, for instance, you want a final resuilt that is A4 size, you can use A3 paper and trim awayt the excess, but that would be very wasteful. Hence, each book(let) has its unique size.

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Note added at 26 mins (2006-05-16 10:13:21 GMT)
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Apologies for the many typos above!

Awana rightly notes that there are also B and C formats. All these strandardised or logarithmic formats refer to trimmed paper (as opposed to rolls of paper which are only cut along their outsides) and are not suitable for other than office and domestic printing, with formal legal, engineering, economic, et c., reports being about the largest items that are suitably printed on them.

For full-fledged machine-printed matter, non-standard trim sizes are chosen for reasons outlined above.

A-format is 110x178 mm.
B-format is 130x198mm.
C-format is 135x216mm.

C-format is also referred to as Trade - except in the US where Trade means B-format.