This parameter seemed to have been first spotted at WebmasterWorld on June 26, 2005. DaveN just posted a thread about it at Search Engine Watch Forums as well. DaveN explains that the "biw parameter in google sets the Browser window in pixels" and shows an example http://www.google.co.uk/search?biw=1004&hl=en&q=DaveN&btnG=Google+Search&meta=.
The WebmasterWorld thread tries to get into why Google is recording this data, and also how. How? Most probably through some JavaScript. They "why" is something very interesting and I wonder why...