Definition
MIDI is short for Musical Instrument Digital Interface and a common protocol of how digital music instruments communicate.
A midi file contains data that comply with the midi protocol.
The strength of MIDI
After more than 30 years on the market midi is still the most flexible format when it comes to producing music.
Midi provides you with the freedom of making changes to already recorded music in a way that no other format has been able to imitate. This is due to the fact that midi only registers information about what is being played and how.
You cannot hear midi per se but the midi information can be send to a sound source which generates audible music when receiving it. Midi is therefore very flexible given that by changing the sound source and the midi data you have full control over the music.
The downside, however, is that without a sound source you cannot listen to the midi music and a proper sound source like Yamaha Tyros5 can be very expensive especially if keyboard is not your prime instrument.
Audio as an alternative to midi
If you do not own a really good sound source you can instead buy MP3 audio backing tracks as this format runs on all music players.