What is it?

YahooWidgetEngine.exe is associated with the cross platform Yahoo desktop accessories application.

What does it do?

From yahoo:
The Yahoo! Widget Engine (formerly known as Konfabulator) is a JavaScript runtime engine for Windows and Mac OS X that lets you run little files called Widgets that can do pretty much whatever you want them to. Widgets can be alarm clocks, calculators, can tell you your WiFi signal strength, will fetch the latest stock quotes for your preferred symbols, and even give your current local weather.

More info:

Read more about yahoo widgets @ widgets.yahoo.com