What the hell is a .mod? A short history of module music
Generically, the term ".mod" refers to a music module or tracker module, although it is also the name of the first file format used to store such files. A tracker module differs from modern computer music because it is a sequence of short samples (and/or synthesized sounds), whereas a modern computer music file is just a single sample. Think MIDI vs. MP3 (although MIDI sequences do not contain any samples, they are just sequences that can be interpreted differently by the hardware and software used to play them). In the days when dinosaurs roamed the Earth and the Commodore 64 was the hip computing platform, all computer music was sequences, although these early computer compositions had no samples, just synthesized sounds. Such chip tunes have their own strange aesthetics, as well as a quite devoted following -- witness the popularity of C64-era SID tunes in the modern computing underground, and bands like Press Play on Tape who play old chip tunes on "real" instruments.
The Amiga era: Sampling and Tracking
When the Amiga showed up, lots of people in the demo scene and game maker communities didn't really feel that the old chip tunes cut it any more, given that the Amiga was quite capable of playing back sampled audio. But on the other hand, storing music as one big sample was seriously limited by the fact that the usual storage medium on early Amigas was 880 kilobyte floppy disks. MODs attempted to give the best of both worlds. You could sample short sounds, typically the sound of a single instrument (a bass note being plucked, a strum on a guitar, a short drumroll, or something similar), and repeat it to a rhythm, alternating the sound's pitch. .MODs had a somewhat "artificial" sound, because such samples lack the minute imperfections and nuances human musicians add to the sound. But on the gripping hand, the demo scene was all about making art on a minimalist computing platform, and both scene and game musicians managed to make .MODs into an art form in itself. An example of this was the chipmod, essentially an all-synthesized MOD with no samples, bringing .MODs full circle back to their roots.
You'd compose your .MOD masterpieces using a "tracker" (or sequencer, although nobody called them that), and there was several possibilities. The Mother of all Trackers was SoundTracker, written in '87 for the Amiga by Karsten Obarski. While SoundTracker development continued, a couple of successful clones were made in NoiseTracker of '89 and ProTracker of '90. Teijo Kinnunnen made a similar, but not identical, music sequencing system in MED and its bigger brother OctaMED. Most x86 PCs around this time were limited to their puny internal speakers for sound output, so tracking software didn't appear on that platform before the early to mid 90's. Nobody could stand listening to those damn internal speakers anyway, they sounded like a flock of mutant geese subjected to the Spanish Inquisition's tender care. ScreamTracker, developed by Future Crew was one popular PC tracker (and one which would later introduce lots of improvements to the original .MOD format). It was also the first tracker made for musicians rather than coders (demo scene musicians tended to be part coder, part musician). FastTracker was another, later, PC tracker.
.MOD tech specs
The first .MODs were limited to four channels of output, a maximum of 15 samples, and a maximum of 64k size per sample. .MED had 31 samples, and by OctaMED it could handle eight channels of output, due to some clever hackery by its maker -- the Amiga only had four audio channels on its built-in Paula sound chip. Later extensions to the .MOD format include .STM, with 16 channels and 31 64k samples, and .S3M, which has 48 channels and 31 1024k samples. Both these were introduced by ScreamTracker. .XM has 64 channels and 63 1024k samples, and came into being with FastTracker. .IT added a few special features to this, for use in Impulse Tracker. Threed mentions the .MTM, .FAR and .669 formats in his writeup, I sadly don't know anything about those. I drifted out of the tracker community around the time when .XM was all the rage.
Like many other such early technologies, .MOD files had a devoted following and a sense of community around them that you don't see a lot of in the modern computer underground. And no politicians or recording industry maniacs were trying to outlaw tracker-mods either. Now I'm going to stop writing before I turn into a wretched mass of computing nostalgia.