Do you mean the checkmark? A check mark ( √ ) means that you want that song available for upload to your iPod, iPad, etc... if you uncheck it, it will still be in your library, but not uploaded.
If you use your library for multiple devices (i.e. - I have a shuffle, iPod Classic, iPod touch, etc), then it's easier to check stuff as available for upload by clicking on the pic of the device. That will show you everything on the device, and have tabs on top where you can check and uncheck what you want to upload by type (movie, music, etc), genre, playlist, artist, etc.
My iPod Classic has ALL of my music and podcasts, but not all of my movies. I move movies on and off of my iPod touch as I watch them... but like a smart list, you can have the iPod touch figure this out for you by setting a smartlist up on the device tab MOVIES to the last X many uploaded, or only unwatched, or whatever. I like to manage mine manually, that's just my thing.
AS FOR YOUR TICK SYMBOL - another thing to check is your VIEW OPTIONS. You can pick what you see in your iTunes screen, such as my love of seeing the upload date, last time played, ratings, etc... I like to see certain data when I'm creating playlists, so I alter my views as I need to do so. It's a great thing!
Hope this answers your question :-)