In the olden days, (La)TeX distributions were limited by the feebleness of file systems' ability to represent long names. (The MS-DOS file system was a particular bugbear: fortunately any current Microsoft system allows rather more freedom to specify file names. Sadly, the ISO 9660 standard for the structure of CD-ROMs has a similar failing, but that too has been modified by various extension mechanisms.)
One area in which these short file names posed a particular problem was that of file names for Type 1 fonts. These fonts are distributed by their vendors with pretty meaningless short names, and there's a natural ambition to change the name to something that identifies the font somewhat precisely. Unfortunately, names such as “BaskervilleMT” are already far beyond the abilities of the typical feeble file system, and add the specifier of a font shape or variant, and the difficulties spiral out of control. Font companies deal with the issue by inventing silly names, and providing a map file to show what the “real” names. Thus the Monotype Corporation provides the translations:
bas_____ BaskervilleMT basb____ BaskervilleMT-Bold basbi___ BaskervilleMT-BoldItalic
and so on. These names could be used within (La)TeX programs,
except that they are not unique: there's nothing to stop Adobe using
bas for their Baskerville font.
Thus arose the Berry naming scheme.
The basis of the scheme is to encode the meanings of the various parts of the file's specification in an extremely terse way, so that enough font names can be expressed even in impoverished file name-spaces. The encoding allocates one character to the font “foundry” (Adobe, Monotype, and so on), two to the typeface name (Baskerville, Times Roman, and so on), one to the weight, shape, and encoding and so on.
The whole scheme is outlined in the fontname distribution, which includes extensive documentation and a set of tables of fonts whose names have been systematised.