For online pages, it looks for a favicon.ico file on the web server and uses it if found (this lookup is done once per domain, if it has already been retrieved previously for that domain, the existing icon is used). This was how it was originally done, and most sites put the favicon there. Later, specifications were defined for other ways to indicate the favicon (see
http://en.wikipedia.org/wiki/Favicon), but UR doesn't support them.
If the favicon isn't found (or when importing local HTML files), it looks for the icon associated with the .htm extension in Windows (this lookup is also done once, and if it has already been stored, the existing icon is used). If no association is found, UR uses a generic document icon.
To force an update of an icon that's already been stored, search on that icon and temporarily change all matching items to another icon (to remove the site icon from the database), import another page from that site, and update all of the stored items to have the new icon.