Source: http://en.wikipedia.org/wiki/Cornett
The earlier cornet (cornett, cornetto) is basically a flute that is blown with vibrating lips, and may thus be regarded as a combination of a flute and horn (or bugle).
In earlier periods (Medieval, Renaissance and Baroque periods) the shape of the cornet was fairly straight, with a slight curve or kink, while the modern cornet may be regarded as a small trumpet.
Earlier cornets
Source: http://en.wikipedia.org/wiki/Cornett
The modern version of the instrument originated in the first quarter of the 1800s when valves were added to the bugle. Today the cornet has valved holes (piston-like) to change the length of the pipe, which is typically wound to make it easier to hold and move. Human lips act as modifiers ("reeds").
Source: http://www.miayf.org/brasswind/cornet/
http://www.youtube.com/watch?v=ma_iW7BYOHE
http://www.earlymusic.co.uk/general/prod_3.htm