Actually the browser window is only useful with SuperEdi scripts. The example scripts in the menu "Tools/Scripts/Browser Window" are intended as inspiration for more useful applications. For example try the script "Preview Document" when active window contains a HTML or XML file.
This one invokes the default action on the document file, i.e. the same action that happens when you double-click on the file name in Windows Explorer. For HTML and XML files it should open Internet Explorer or whatever your preferred browser is. It will not work if the file is new and has not been saved yet.