RSS is a popular format for news feeds. Web sites with frequently updated content can make it available as a (RSS) news feed, also known as syndication. Anyone interested in following syndicated content can subscribe to it, and will then automatically get all updates to that feed.
To read feeds you subscribe to you need a feed reader (or news reader, or aggregator). There are online feed readers that you can sign up to, or you can download and install a standalone reader. Actually, most modern web browsers (like Firefox, Safari, Opera, Internet Explorer, but not Chrome) and e-mail clients (like Thunderbird, Apple Mail, Outlook) have built-in feed readers.
News feeds are often identified with an icon like thison web sites offering the feed.
To subscribe to a feed, click on the feed link and follow the instructions, where at some point you will be asked which feed reader you want to use for this feed. If nothing sensible happens when you click the feed link, you can instead copy the feed address and paste it into your feed reader (check your reader's help section for instructions on how to do this).