Paul Bishop posted this project in the arduino blog. A microphone is connected to a transistor amplifier, and the output is driven to the analog input of Arduino. These data are converted then into digital values, and are captured over time. The captured data are then processed with what is known as Fourier Transformation. This process generates a good picture of the audio signal, which is then displayed in real time on a TV, through an NTSC video-out signal. Read more details here.