As explained by Alan Polivka  in his Accordion FAQs

MIDI accordions are the latest and greatest thing (albeit, they've been around for multiple years now) in combined electronic/acoustic accordions. You can play all your standard MIDI synthesizers (whether rack-mounted, standalone module, or having a keyboard attached) from a MIDI accordion, (rather than from a typical horizontal keyboard, for example). Of course, you can also get the original acoustic accordion sounds as well.

MIDI (Musical Instrument Digital Interface) is a serial (electronic) bus standard established for musicians. A MIDI accordion is equipped with a switch on each key and button. A small circuit board is all the electronics required inside the accordion, so there is minimal weight added to the accordion. It scans the keys and sends out MIDI "Note On" or "Note Off" messages every time it detects a change in state of a key (every time a key is pressed or released, respectively). There are, of course other types of messages sent out too (e.g. for selection of patches, pitch bending, volume control, etc.).

The MIDI cable that connects your accordion to MIDI synthesizers is just a relatively thin cable (not a heavy cable like used on the old Cordovox accordions). You can even get wireless transmitters for a MIDI accordion so that you have no cable going out of it at all.

One of the biggest advantages of MIDI for accordions is that synthesizer technology is evolving at a much more rapid rate than is acoustic accordion technology. So, if you have a standard (acoustic) accordion that you really like, you don't need to trade it in every time there are improvements in the synthesizers. You keep the same accordion and just upgrade synthesizers. Since companies like Yamaha, Roland and Korg have such huge markets for synthesizers (in comparison with the accordion market), there is a ton of money going into R&D developing really impressive synthesizer technology that the MIDI accordionist can take full advantage of. Further, you only need the synthesizer module (no keyboard needed) which saves you money on the synthesizers.

Another nice feature about MIDI accordions is that they make an ideal MIDI controller (in some ways better than a typical keyboard controller). I have both, a keyboard controller and a MIDI accordion, so I can attest to this first hand. Separate MIDI channels can be set up for bass, chords, treble, solo, making the accordion into a 5 piece band (counting the acoustic accordion as one instrument).