Simply, it means, musical instrument digital interface. An instrument converts the sounds that you are trying to perform and turns them into 1's and 0's.
It takes what you are doing on either your keyboard, or other device and puts data into Attach, Decay, Sustain and Release categories.
When you think about sound and how it happens, you can think about: Attack (making the sound); Decay (how does the sound decay after the initial attack); Sustain (what the sound sounds like - does it grow, swell, dissipate, swirl etc.); and, Release (when we release from the sound).
These are terms that we have been using for a while now in sound synthesis. In that case, we have taken raw electric sound signals and have made sounds out of those combinations. We called those electronic contraptions, synthesizers.
(BTW - That's why we call a Drum Kit a Trap Set. Trap is short for contraption. The More You Know (cue NBC theme)).
Major and massive improvements have been made to the instrument interfaces and the software that interprets all of this data.
One of those instruments that have made significants strides in this area is the Yamaha Hybrid Piano line. More to come on this incredible instrument. I had the recent blessing of acquiring the N2 model. And, I'm just getting started in learning its capabilities.