Correct spelling is, of course, Fluegelhorn.
A brass instrument similar in appearance to a trumpet but with a gradual taper in its diameter along the length, rather than the more abrupt opening on a trumpet.
The sound is warmer, softer and darker than that of a trumpet.
I think that the name comes from the German word "fluegel" which means wing. Fluegel is also used in German for a grand piano due to its shape, so I imagine that the gradually flaring shape of the fluegelhorn gives it its name.
See also, musical instruments.