Source:
http://en.wikipedia.org/wiki/File:Bassoon_Reeds.jpg
Many air instruments have a "reed" in the mouthpiece that vibrates when blowing across it. The vibration causes a soundwave. Acoustically this is known as the Bernoulli Effect.
Traditionally the "reed" was a small strip cut from natural materials such as a piece of bamboo, reed or other material. The English word reed reflects the use of cane reed. Today "reeds" are made of articifial materials ranging from metals to plastics.
"Reed" instruments should perhaps rather be described as "instruments with resonating modifiers".
The reed is typically fastened at one end, leaving the other end free to vibrate.
Some instruments have one reed (clarinet and saxophone), some have more than one reed in the same pipe (oboe, cor anglais / english horn, bassoon, shawm and bagpipes), some have multiple reeds, each in its own pipe (accordion, harmonica).
The material, shape, method of fastening the reed to the instrument (typically to the mouthpiece) and the materials used to fasten the reed all influence the resulting soundwave.
Source:
http://en.wikipedia.org/wiki/File:Bassoon_Reeds.jpg
Source:
http://en.wikipedia.org/wiki/File:Saxophone_reeds-alto,_tenor.jpeg
Source:
http://en.wikipedia.org/wiki/File:Oboe_Reed.jpg
Source:
http://en.wikipedia.org