UPDATE 30/07/2010.
I've found a few interesting posts and comments on this topic:
http://originalprojects.com/projects/shazam-for-birds
The comment by the user 'nature' is interesting http://www.tuaw.com/2009/02/09/this-iphone-app-is-truly-for-the-birds/
An education app http://itunes.apple.com/us/app/chirp-bird-songs-usa-lite-v3/id352826689?mt=8
UPDATE 05/05/2011
This blog posts explains in a neat way how Shazam works: