MOD is short for Module.
MOD file is essentially one of data-format of SoundTracker that is software for composing music on AMIGA. SoundTracker have two data-format, Song-format and Module-format. Module-formated file contains data of tone and score, Song-formated file contains data of tonename and score.

MOD is also short for "Microsoft Official Dealer" :-P

N.H.K.'s MOD PAGE(About MOD)