A widget is anything that can be embedded into a web page or applications that are installed on a desktop, usually from a third party, delivering live content (advertisements, links, images, news) to the user's desktop without the website owner having to update it.
They are slowly becoming a distribution or marketing channel for companies. The opportunity that is sometimes overlooked is that a branded widget may stay with the user for months or years after the campaign it was originated from has disappeared.
In order to develop widgets, a level of technical skill/understanding, that is not commonplace in standard digital agencies, is required and this is one reason for their slow proliferation. The opportunity that they present will of course ultimately win the day.
Have a look at Yahoo Widgets for some standard examples. And have a look at UPS for a great commercial application of a widget.