Actually, gargoyle, there are a number of nose flutes, but the kind most people here are talking about is a plastic gimmie that is designed to butt up against the bottom of your nose and cover your mouth except for a whistle hole. YOu exhale thru the nose apperture (no colds allowed), and shape the tone and pitch with your open mouth. Makes a very silly noise, a straight tone with very little vibrato that sounds something like a slide whistle.
The nose connection is usually a flat rectangular shape with a flange that seals it to your nose, and the mouth shield part is an slightly curved oval to fit it to your mouth. maybe 3 inches each way. You have probably stared down at them when you cruised the harmonica-jewsharp-fingerpicks-and-other-little-instrument-bits case in your local music store. Next time keep a straight face and ask, and I bet they'll have one.
However, the some cultures of the East, India and others, believe that the breath of the nose is more pure than that of the mouth and have designed a number of 'normal' looking flutes to butt up against the nose rather than being played by the mouth. So those also are 'nose flutes'.
Blessings,
Barbara