M.I.D.I. stands for Musical Instrument Digital Interface.
If you are a band/person that is totally happy with how you currently produce music then I'd recommend that you don't go there.
But if you fancy the idea of hooking up loads of different electronic musical devices such as synthesizers, drum machines and samplers then MIDI is the way to go.
Some of the advantages of MIDI are:-
a) The data stored to capture a performance is much much smaller than audio data.
b) It's so easy to make changes such as pitch or tempo and there are no issues with time stretching that you would get with audio files.
c) You can tweek like hell, adding pitch bend effects plus much more without having to re-record your session. Your sequencer play back all your data the same each time and if you don't like those tweeks then it's easier to remove them.
Disadvantages are:-
a) MIDI music is sometimes frowned upon as being mechanical and played/programmed by people who are not "real" musicians.
That's all I can think of for now.
I can go into more detail if you wish, about the data that is stored for instance...
andy