When you try to empty the trash, or move a document (text file, image, whatever) and the OS thinks an app has it open, you'll see this message. Moving it anyway won't hurt the app at all. Although, if the file still really is open in the app, you'll sure confuse it.
This problem used to show up much more in older versions of the Mac OS, when it became OS X. I rarely see it anymore, but occasionally, you'll get this message even when you know you've closed the file you're moving and no app has it open.
There's no need to Force Quit apps. Just Command+Tab to each one and first check to see if a given app really does have the file open yet. If it does, close the file. Either way, then close the app normally.
Even this doesn't always help. I've had the Mac down to just the Finder, and the OS still wouldn't let move move a file, or empty a particular file or two in the trash. At that point, simply restart the Mac. That will always release everything.