According to Wikipedia, a web widget is a third party item that can be embedded in a web page. Widgets can be syndicated and supply many websites with fresh content, entertainment (i.e., games, picture of the day, music), or a helpful web tool (i.e., a mortgage calculator, language converter, site search).
Widgetbox and Yahoo Widgets have 1000s of free web widgets to add to any website. For example, this blog has several web widgets located on the right hand panel. AnswerTips, provides a way to double-click on any word within this site to receive its definition and pronounciation. (Check out our post about AnswerTips). And currently we are testing both the Sphere Blog Search and the Google Site Translator.
If you are unable to find the widget that will work for you, you can have one created and distributed online through RSS and sites like Widgetbox to draw new traffic to your website.