It's an instrument tuner
The DSi wasn't intended just for games; part of the meaning of the "i" is in reference to using it as a "personal tool," according to some Nintendo rep who may or may not have been full of it. We've already seen some fairly useless applications hit the service already, lending credence to this, so it makes a weird sort of sense for Nintendo to roll out..
About The Game
The Nintendo DSi Instrument Tuner software can be used to tune an instrument by aligning tonal pitches.
The software offers two methods of handling this: feeding sounds into the microphone to measure the difference with a target pitch, or listening to a sample tone. In addition, the standard musical pitch and notation can be changed, as well as the design of the tuner (choose one of three designs). If you're feeling especially in tune, test your ear by taking on the Tuner Fight minigame's challenge: Pop balloons as they rise from pipes by making tones that match the displayed pitches.