iTunes' Visualizer displays abstract computer graphics while your music is playing. This can be entertaining in full screen, in a social setting, when a computer is used purely to play music (think Party Shuffle).
To turn on iTunes' Visualizer, choose Show Visualizer from the View menu. (The item label becomes "Hide Visualizer" if the Visualizer is currently displayed inside iTunes.) If the Show Visualizer menu item is disabled (grayed out), you are probably in a section of iTunes that does not support the Visualizer (like the iTunes store); just switch back to Music, for example.
Keyboard shortcut: to display or hide iTunes' Visualizer, hit Ctrl+T (Windows) or Command+T (Mac).
For the first few seconds after turning on the Visualizer, iTunes will display the Apple logo and the song information in the lower left corner. Progressively, after the first few cycles of animation, the logo and song information fade away. To fully experience the Visualizer, choose View > Full Screen from iTunes' main window.
Keyboard shortcut: toggle full screen mode on or off by pressing Ctrl+F (Windows) or Command+F (Mac).
There are a few options pertaining to the Visualizer, which are not located under iTunes' Preferences window. Go to View > Visualizer > Options... to configure custom settings. The Visualizer Options dialog will open.
These Visualizer Options dialogs show iTunes' default settings on both Mac and Windows.
The Display frame rate option is off by default; if checked, it tells iTunes to display the current rate of frames per second displayed through the Visualizer. The frame rate appears in the upper left corner of the window/screen.
By default, iTunes limits the power processing needed to display Visualizer animations, and the Cap frame rate at 30 fps (frames per second) option is off by default; if your computer's video card is solid (128 dedicated megabytes or higher), you will experience flawless animations, much more creative than otherwise (with the frame cap on).
The options Use OpenGL (Mac) and Use DirectX (Windows) allow iTunes to use the operating system's built-in acceleration engine for 3D effects in the Visualizer. For more peppy animations, check the Faster but rougher display; the animations aren't that rougher if you have a fast processor and video card; here too, they are more interesting with the option turned on.
The Always display song info checkbox (unchecked by default) instructs iTunes to maintain the album artwork and title floating above the Visualizer's background animations. When this option is off, iTunes fades out the album cover and information after a few seconds of animation. The Apple logo, however, fades away as normally, without being affected by this option.