Audioscrobbler is a computer system that builds up a detailed profile of your musical taste. After installing an Audioscrobbler Plugin, your computer sends the name of every song you play to the Audioscrobbler Server. With this information, the Audioscrobbler server builds you a 'Musical Profile'. Statistics from your Musical Profile are shown on your Audioscrobbler User Page, available for everyone to view.
There are lots of people using Audioscrobbler, but usually only the people who like the same sort of music to you are interesting. The Audioscrobbler Server calculates which people are most similar to you, based on shared musical taste, so you can take a look at what your peers are listening to.
With this information, Audioscrobbler is able to automatically generate suggestions for new songs/artists you might like. These suggestions are based on the same principals as Amazon's "People who bought this also bought X, Y, Z", but because the Audioscrobbler data is what people are actually listening to, the suggestions tend to make more sense.