Please note that the following solution for this problem has been found to work for iTunes 12.4.2.4 for Windows. If any other people using versions of iTunes newer than 11 up the the current version for Windows or the current version of iTunes for Mac OSX that want to append anything to this old thread by all means do so.
The setting that
TH55 has tripped is simply the "Up Next" function which is triggered when you right-click on a song and select "Play Next" instead of double-clicking on the file so that it "Plays Now". Once you clear the "Up Next" queue of items, the problem goes away.
PS: This message is probably 3 years too late for TH55, but for anyone else getting this message:
"You are about to start playback. Do you want to clear the <songs in Up next queue> songs previously added to Up Next?"...
View attachment 643443
...press the "Up Next" button (shown below glowing in
blue),
View attachment 643446
...then keep clicking the "Clear" button until the "Up Next" list of items is completely empty.
View attachment 643449
If you've followed this process correctly, the "Up Next" button will change from a
blue glow to the usual grey.
View attachment 643450
Problem fixed! Now you can double-click the file name to play what you want without the "You are about to start playback" message.
More info from CNet about how to use the "Up Next" function (introduced in iTunes 11):
http://www.cnet.com/au/how-to/how-to-use-the-new-up-next-feature-in-itunes-11/