According to the Wikipedia:
The kazoo is a wind instrument which adds a "buzzing" timbral quality to a player's voice when the player vocalizes into it. The kazoo is a type of mirliton, which is a membranophone – a device which modifies the sound of a person's voice by way of a vibrating membrane.
"Kazoo" was the name given by Warren Herbert Frost to his invention in Patent #270,543 issued on January 9, 1883. In the text of the patent he refers to it as "This instrument or toy, to which I propose to give the name 'kazoo' " (see picture at left).
In order to play the kazoo one should be humming into the kazoo. Blowing with the lips closed around the mouthpiece of the kazoo will not create sound – one must vibrate air from one's lungs by humming into the instrument to produce a sound. Increased air flow and harder blowing will result in a louder sound.
Historically such instruments have been used in Africa for hundreds of years, to disguise the sound of somebody's voice or to imitate animals, often for various ceremonial purposes. Today it is widely used by folk and minstrel singers, jazz and blues player.
There is a wide fare of different kazoos, from 1$ (or less) plastic or metal one (pic. at left) up to 50$ (or more) artistically curved wooden one.