Update: Newzbin.com closed down in November 2012. They say they will be re-opening soon with new services. The information below applied to the old site, and it may or may not apply to the new site when it re-opens.
Aside from NZB files, you don’t download files from Newzbin.com. Newzbin is a search engine, and what it searches is a network called Usenet. When Newzbin finds what you want, it will put a list of pointers to all the parts into an NZB file. Then, you download that NZB file, and feed it into NZB-downloader software like Super-NZB.
And in order for the NZB downloader program to work, it needs to have access to a Usenet server, such as Easynews.
For more details, see this page: “Learn to Download NZB Files.”