What is the significance of the tick boxes beside items in my iTunes music list?

Francis, Mostly you can leave them checked and ignore them. However, note that (1) when playing, iTunes will not automatically advance to an unchecked song (2) unchecked songs will be excluded from Smart Playlists if "Match only checked items" is applied, and (3) unchecked songs will also be excluded from iPod syncing if "Sync only checked songs" is chosen.