With iTunes 8, Apple introduced a new feature called Genius. Genius provides two different functions for iTunes users.
First, Genius serves as a marketing tool by suggesting songs in Apple's iTunes Store that you might wish to purchase based on currently selected tracks (much like the iTunes Mini Store feature in previous versions of the software).
Second, Genius allows you to select a single song and build a playlist around it. The "genius algorithms" that Apple employs should generate a playlist of songs that, as Steve Jobs put it, "go great together".
How Genius Works
Apple hasn't yet made the details of how Genius works public knowledge. What is known is that it is an opt-in feature that users must choose to enable.
Once enabled, iTunes will analyze details about the music in your iTunes library and transmit that analysis to Apple's iTunes server (where it is compared to similar information from other iTunes users), which will in turn deliver a file containing "Genius results."
These results are what iTunes uses to suggest songs and to build playlists. The results appear to reside in a file called iTunes Library Genius.itdb, located in the same folder as your iTunes library files. Genius results are updated on a weekly basis via the same process.
Apple has been very quiet about what information it uses to generate Genius results, although the company has said it does not include personal information in the data used to analyze music or deliver results.
The majority of this information is stored as "tags" for tracks in the database used by iTunes to maintain your library, which iTunes also uses to locate and organize music and other media.
Activating Genius is as simple as selecting a song in iTunes and clicking the Genius icon (which, like the symbol for the Genius Bar in Apple's retail stores, resembles an atom).
When activated, a bar appears over the Genius playlist, indicating the song on which it was based and providing a pop-up menu to adjust the length of the playlist (the default length of 25 sounds can be changed to 50, 75, or 100 songs); a button to refresh the contents of the playlist without changing the song on which it is based (essentially reshuffling the list); and a button to save the playlist as a traditional playlist that can be used later or synced to an iPod, iPhone, or Apple TV.
The current release of iPhone/iPod Touch firmware, as well as the current release of Apple TV software and the most recent iPod models, also support the Genius feature (though they do so by syncing the contents of the Genius database file onto the device to generate Genius playlists).
For iTunes Store recommendations, the Genius Sidebar can be toggled off and on using the left-facing arrow button in the lower right of the iTunes window (right next to the Genius button).