Really Simple Syndication (RSS) is an XML-based format for distributing news or other information direct to web sites or news readers.
It will allow you to subscribe to news headlines, or to have those news headlines appear on your web site.
To get an RSS feed from this web site, you will have to install a 'news reader' that displays RSS feeds from web sites you select. After installing the news reader, you can add a feed from each web site by clicking on the "XML" orange button next to the feed.
Recommended news readers:
The Firefox browser is a great tool for this kind of thing. More info at: http://www.mozilla.org/products/firefox/live-bookmarks.
Another recommended newsreader is at http://sage.mozdev.org/. It is a newsreader embedded in the sidebar of the browser. Easy to add to and nice to view. Can't go past it.