Jez Swanson, an engineer at Google, wrote a very pretty explanation on how Fourier transormations work and what their role is in storing sounds and images.

The Fourier transform is an extremely powerful tool, because splitting things up into frequencies is so fundamental. They're used in a lot of fields, including circuit design, mobile phone signals, magnetic resonance imaging (MRI), and quantum physics!

http://www.jezzamon.com/fourier/index.html