A "tracker" is a piece of music composition software, sort of a glorified spreadsheet. Imagine a virtual piano roll, with note and instrument data laid out over time.
The vast majority of tracker music was initially in a format called MOD, since it originated the format. MOD's specification was matched to the capabilities of the Amiga sound chip, which proved limiting as time went on, so other formats emerged. Formats and file extensions now include STM, S3M, XM, and countless more. The collective term "tracker music" is easier than trying to enumerate them all.
Trackers are differentiated from note-data formats like MIDI in that a tracker song includes the samples themselves, little snippets of WAV-like data which are played at sped-up or slowed-down sample rates according to the note data. Whereas a MIDI file only includes the notes and timing information, which gets sent to "instruments", which are responsible for translating those commands into sound. Different instruments may do it differently, so a MIDI can sound vastly different depending on what player you're using. A tracker song will sound roughly the same everywhere, barring bugs, with the only difference being that certain player software may have higher-quality math (higher CPU usage) for the sample-rate adjustment and mixing.
Because of their self-contained nature, containing only the sound samples actually used in a given song, tracked music was popular in video games and in the game cracking scene alike. (All the music in Star Control 2 is embedded MOD files, for instance.) And like anything else in what became the demo-scene, the mantra of doing more with less, making enjoyable music in just a few K of note data and samples combined, became its own factor to compete on.
Modarchive.org is the place to go to experience tracker music now; there are players that run in your browser. Click through the top couple songs and you'll get a feel for not just the format but also the era, since the heyday of MOD was the early 90s, much of it fits right into what we now nostalgically think of as 90s electronica.