Open up the ES File Explorer application (it'll be listed when you click the icon of a circle with six dots or the My Apps shortcut) and expand the LOCAL menu on the left. One of the last entries shown will be your USB device (assuming you've already plugged it into your DroidBOX!).
You can cut/copy and paste files to and from the drive, either using your DroidBOX (long click a file to select cut/copy) or your PC.