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From The Jargon File (version 4.4.7, 29 Dec 2003) [jargon]:
magic number
n.
[Unix/C; common]
1. In source code, some non-obvious constant whose value is significant to
the operation of a program and that is inserted inconspicuously in-line ({
hardcoded}), rather than expanded in by a symbol set by a commented #define
. Magic numbers in this sense are bad style.
2. A number that encodes critical information used in an algorithm in some
opaque way. The classic examples of these are the numbers used in hash or
CRC functions, or the coefficients in a linear congruential generator for
pseudo-random numbers. This sense actually predates and was ancestral to
the more common sense
3. Special data located at the beginning of a binary data file to indicate
its type to a utility. Under Unix, the system and various applications
programs (especially the linker) distinguish between types of executable
file by looking for a magic number. Once upon a time, these magic numbers
were PDP-11 branch instructions that skipped over header data to the
start of executable code; 0407, for example, was octal for ?branch 16 bytes
relative?. Many other kinds of files now have magic numbers somewhere; some
magic numbers are, in fact, strings, like the !