MIDI is just a communications protocol. That gizmo just basically enables your DS to talk that language. It's primary use is to be able to sync/control your DS from another source (computer, other gameboys, a dead cat wrapped in ham). I don't know much about music on gameboys but I'm fairly certain there's more than a few music software that support sending midi data in and out. You can use that device to.. for example, load up Korg DS-10 and play it from a standard MIDI controller keyboard, or sync up two gameboys together.
From the website, their interface supports converting MIDI input into button presses, which means you can pretty much control anything you'd normally do on a DS, from an external device. Hell if you're patient enough you could compose a song that plays New Super Mario Bros from start to finish