Defined in 1982, MIDI is a standard protocol that allows multiple electronic instruments and musical devices to communicate and synchronize with themselves. It is usually associated with the sound of the Microsoft GS Wavetable Synth, which is the soundfont midis are to be rendered to on BOTB.
A composition saved as a MIDI is a sequence of notes and commands that will be played back by the computer's own midi drivers. Since this makes a .mid file much smaller than an audio file, midi files have a rich history of use in computer games, software, web, et cetera.