Normally when you download a widget and double-click it, you are presented with a dialog to install the widget. You can either cancel, and exit the installer, or click install, and the widget is moved to you widgets folder (Library/widgets).
However, in some situations you don't want to move the widget. For instance if you are trying out a widget and don't know if you want to keep it, or you are developing a widget and are just testing it out. To stop the widget being installed, hold down Command and Option while double-clicking it. Instead of an install button, you are presented with Run, which, funnily enough, allows you to run the widget without installing it.
Clicking this opens the widget up in dashboard, but it isn't moved to the widgets folder, instead running it from wherever you downloaded it to.
As a result the widget won't be in your dashboard bar, so it is a nifty trick if you want to save scrolling through loads of widgets (especially if you are a dashboard addict). This also means that once you have closed the widget, its gone for good, and you can't open it up from within the dashboard. Of course its still sitting in your downloads folder, so a quick Command-Option-Double-Click will have it open and running again.