How can I get a list of webpages that contain the image in question? Photobucket has a stats option which lets you see what websites have embedded your image. How do they do that?
I'd assume photobucket checks the webserver logs, looking for the referer in any request for a specific image.
For any HTTP request, the browser also sends the so-called referer which contains the URL that "triggered" the request. If someone clicks on a link to webpage B in webpage A, the browser not only requests the linked webpage from the server of webpage B, but also sends the referer along, containing the URL of the "linking webpage" A. Same goes with images embedded in a webpage. The request for the image also contains the URL of the embedding webpage so the server can log which pages embed an image.
Of course, this could be suppressed by privacy tools in the user's browser, so the method would not be completely correct, but in most cases its sufficient.
My guess is that they're seeing what web pages are pulling the embedded image by parsing the server logs.