For Web 2.0/Social Networking 2.0, a good definition and example of a widget can be found on the NBA site.
What is a Widget?
According to Wikipedia, a Web Widget is a portable chunk of code that can be installed and executed within any separate HTML-based web page by an end user without requiring additional compilation. Web Widgets can be utilized by end users to enhance a number of web-based hosts, or drop targets. Categories of drop targets include social networks, blogs and personal homepages.
A widget that displays updated NBA scores in my blog.
A widget that displays information on NBA player, Dwyane Wade that includes updated news.
As many of my friends know, I'm an fanatic Miami Heat fan and you'll find me at the American Airlines Arena for the playoff games this year. Go Heat!