A long time ago I installed the Art Directors Toolkit widget. Today, when I restarted my computer after a power outage, there were 2 instances of the widget. The first one is in the dashboard and a second appears on the desktop, like any other application would appear. I don't know how to remove it. It has none of the usual dashboard buttons and it reappears if I relaunch the Dock.
Apple allows widgets to be displayed on the desktop in order to allow the people developing the widgets to test them without using Dashboard. Your system must have had that capability turned on somehow and that widget set to run on your desktop.
To get the widget off your desktop: click and hold on the widget, then press F12 to enter Dashboard. Once Dashboard is active, release the mouse from the widget. The widget is now docked in your Dashboard instead of on your desktop.
You'll probably have two copies of the widget in Dashboard now. You can get rid of one in the normal way (press the plus button at the bottom left and click the
Now, to prevent other widgets from escaping Dashboard in the future:
If, on the other hand, you want to run some widgets on your desktop, you can run the above command with