It's the system used in the Netflix competition. Many modern recommendation systems use it.

Basically, it comes up with categories based on the data. For example, looking at certain movie selections, it can come up with a ranking of all movies "for people who like action movies, but without too much gore." But that topic would be completely inferred. It doesn't know anything about the content of any of the movies, but some things come into pretty good contrast with it. Other lists that it generates are just inscrutable, and perhaps noise, but who knows?

It seems Apple's twist is the *sequence* of songs played (unless people are reading too much into what they hear) and not just the selection of songs to play. So, maybe it's using something like Markov chains or some pairing of things... Oh, I don't know. Maybe there's a paper saying exactly what it does.