RSS (which stands for "Really Simple Syndication") provides a means for people to stay in touch with a website's content without needing to revisit the site to see if anything has changed.
If you're interested in a website with topical content that changes frequently (e.g. news stories or articles), it's easier to subscribe to that site's RSS feed than to revisit it every few days to check what's new.
How do I view an RSS feed?
You can download an RSS Reader from the Internet - there are many free ones to choose from, Google Reader being one of the most common.
RSS Readers work in a similar way to email clients such as Outlook: unread items from the feeds you subscribe to are highlighted in bold. If you click on the item, you can read a short summary within your reader software and then click on a "read more" link to view the full content on the originating website.
If you prefer, recent versions of both browsers (Internet Explorer, Firefox, Safari etc) and email clients (Outlook, Mac Mail etc) allow you to subscribe to an RSS feed.
How much does it cost to subscribe to an RSS feed?
Nothing. When people talk about "subscribing" to a feed, they are referring simply to the process of following a website's content. There's no money involved.
Why subscribe to an RSS feed instead of using bookmarks?
When you bookmark a website that you're interested in, the onus is on you to revisit the site often to catch up with what's new. If you don't do this, you'll miss out on recently-added content.
With an RSS feed, a summary of new content is sent to you automatically and you can choose whether you want to click through to the originating website to read the full content.