An introduction to computer audio
Acoustid is a database containing acoustic fingerprints.
It is an open source project by Lukáš Lalinský.
Internet databases like MusicBrainz use it to identify a song by its audio content instead of tags.
The basic idea is to represent music as a picture.
Transform the audio into a spectrogram using short-time Fourier transform and you have the picture.
Convert it to notes and do some filtering.
This is way too large for a database so compress it by making a kind of audio thumbnail.
For a more detailed description see How does Chromaprint work?