MIDI is an acronym that stands for Musical Instrument Digital Interface, also sometimes interpreted as Musical Instrument Device Interface. The idea behind MIDI came from Dave Smith. The first MIDI specification was released in 1984. The purpose of MIDI is allow different digital devices to interconnect with one another and with a computer. The most common application of MIDI is a keyboard controller connected to a computer and through which an individual can, by playing the keyboard, send that information as a digital signal to a computer program for live playback or for storage and later manipulation.
More information about MIDI is available in this Wikipedia entry on the "Musical Instrument Digital Interface" and through the MIDI Manufacturers Association.