Q: In iTunes what does the check box next to the name of the song represent?
A: The checkboxes in iTunes are used to indicate whether an individual track is included in playback and synchronization. When a track is UN-checked in iTunes, it will be skipped over during normal playback and can only be listened to if you specifically select it.
Unchecked tracks will also never be displayed on or synchronized to an Apple TV device. You can also optionally exclude unchecked tracks from being synchronized to your iPhone or iPod by enabling the Sync only checked songs and videos option found on the Summary screen for your device in iTunes.