Why the checkmarks in the Music I Tunes?

[Ritter 197]

When I open ITunes I see a number (most, but by far not all) of my songs
check marked. What does that mean? In EDIT and Select All it cannot be
turned off, only individually clicking on these checkmarks will "erase"
them. That is too much for over 800 songs.

 

[yeti]

Usually when songs are checked it means they cannot be found. It happens if
you happen to move songs from a folder from which they were originally loaded
into Itunes from. Try and click a checked song (in itunes) and see if it says
'not found'

 

[Ritter 197]

That does not to seem the reason. When I click for instance on Beethoven
Piano Certo (which has this checkmark) it starts playing.
I can also uncheck this mark and recheck it.
But nowhere does it say what it is for or what it does or mean.