The Headline News gramplet reads the wiki HeadlineNews page once every hour. The links from the wiki will appear in the gramplet and clicking them will open the associated webpage in a browser.
Because the Headline News gramplet gets its information from the GRAMPS wiki (at http://gramps-project.org) you need to have a internet connection for this to work. If you don't have an internet connection, then the Headline News gramplet won't show any information.
When you do have an internet connection, the Headline News gramplet will show you the latest headline news about GRAMPS.