MIDI stands for Musical Instrument Digital Interface.
A MIDI file doesn't contain actual audio data, but rather contains commands that let MIDI-capable synthesizers re-create a specific musical passage. The MIDI protocol has been used for years as a way for electronic musical instruments (like digital keyboards and sequencers) to communicate with each other.
Computer sound cards typically feature the ability to interpret MIDI files into music. Since they don't actually contain the music itself, but rather the commands used to re-create music, MIDI files are a lot smaller than audio files like MP3s, WMAs, or WAVs. MIDI files are small and manageable enough that it's not uncommon to find them embedded in web pages, adding a sonic element to the surfing experience. MIDI files usually appear with the ".MID" filename extension.