Was wondering about this function for some time now, well you need to do few stuff first before you actually get the page ontop. First… go to account setting and look for “Download Your Information” from there on I think they double confirm if you want to do it. After confirming the action, they send you the link from the email you use to register for your Facebook account. On that link you be directed to a page just like the screenshot above which would ask for your password. Then after entering it u can download the zipped file which contain few folders html, photos, videos, index.html & README.txt.
My zipped file is around 160mb, so if you got tons of pictures & video. I suggest you download it at a friend house which has a very fast connection. The only reason I see why someone would use this function is when they want to create a whole new account ( dunno for what) or when that person just want to download all his pictures and video into the hard disk because the original was deleted or something happened to the placed it was stored.
Anyway do delete the file after being downloaded if it is not ur laptop or pc. Because everything be downloaded including the private one too.