A production code, also sometimes called a product code or just a White Wolf number, is a code typically found on the spine of a book, or above its UPC code. For those products without one or both the above, it is usually found elsewhere on the packaging. Prior to 2003, most of these numbers were four digits. However, in the 21st century, five-digit numbers became far more common; Orpheus, the revised Dark Ages setting, Exalted Second Edition and the Chronicles of Darkness (the "New" World of Darkness) were all given five-digit production codes. Here on the White Wolf Wiki, we standardize production codes to five digits, adding a 0 to the front of older four-digit codes.
Production codes are used by a company as a standardized way of keeping track of stock (in the absence of the ubiquity of UPC codes, and easier to remember). A fan might use the code to keep track of which items they're missing from their collection, or a retailer or distributor might use them to order stock.
Some companies, such as the defunct TSR, assigned a range of numbers to a particular game line, and then the numbers would progress more or less sequentially. White Wolf, however, while they do tend to assign a number range to a given game line (for example, the 04000-series for Mage: The Ascension), the specifics are somewhat more arcane and unknowable to the public. Thus, while 04600 was be the Revised Edition rulebook for Mage, 04047 was still released afterwards.
Note that the oldest products released by Lion Rampant prior to its merger with White Wolf did not have production codes, as the company was still very much a small-press operation at the time. Even after Lion Rampant began issuing production codes (numbered in the LR 500 to LR 1600 range), they still lacked ISBN numbers until the White Wolf merger.
See also a full list of production codes currently known.