Can't unmount disk

The problem is that something is being used by something on that disk. The 'easy' solution is to restart the computer. Worse case scenario you can hold the power button to force-shutdown the machine.

The more detailed solution needs some more information.

What is on the disk? Is it a disk image (mounts when you open a .dmg file), or a physical disk. Is it an optical disc (CD/DVD) or is it an external HD.

One thing you can try is this...
Launch Terminal (found in /Applications/Utilities)
Type the following...
lsof | grep whatever
...replace 'whatever' with part or all of the name of the disk. If the disk is named SuperWidget then you can use Super or SuperWidget in place of 'whatever'

This will show you the names of programs and/or files that are open on that disk. You can then attempt to quit the program, or programs that have the files open.

A common scenario is you are running a program that is on a disk image (.dmg file). An example might be if you download Firefox and don't copy the program from the disk image to your applications folder. But drag it to the Dock, or run it from the disk image. I've seen this a lot, and so has Apple (in 10.5 you get a dialog asking if you're sure you want to run the program off a disk image).