Shazam: How does it works?

With the iPhone, phone or smartphone application Shazam, you can identify music tracks played on radio, TV, CD PLayer, Movies, etc.. 

Where ever you are, at home, in a store, in a movie theater or in your car hold your iPhone next to the speakers and in 10 secs Shazam identifies the song (Song and Album titles, Artist name), shows the cover and links you to the iTunes store or YouTube to watch the video.  

Last night, I was at my friends Pascal and Christian for a wonderful diner. We were 9 around the table when I was ask to show how Shazam works on my iPhone. After being impressed everybody was wondering how it works. I started to explain.......