Comment 19 for bug 81239

This has been a problem with Linux machines for a long time, even before it was officially a bug. In fact, I've seen the same issue on a Mac as early as 1990 or so:

Mount a drive, launch something that uses one of the files on it, and try to unmount the drive again. This causes an error message saying the drive can't be unmounted because a file is in use by an application.

The problem is that there is no indication of what application has the file open, or what file it is. So if you've been working a while since last using the application, and you have a bunch of applications running, it can become a real hassle to hunt through everything to try and figure out what the holdup is. This usually seems to happen when you're in a hurry to go somewhere and the mounted drive is a USB stick on your keychain along with your car keys!

As nasos wrote, if you have root you can open a terminal and grep the output of lsof. This is the approach I generally use. But it's not much good for a newbie, or for a user who doesn't have root.

SUGGESTION: This step should happen automatically, and the error message in the dialog should say what file(s) are open on the partition, and what app(s) are responsible.