So... what is RSS and what do we use it for?
A quick search over the internet will turn up lots of conflicting definitions. "Really Simple Syndication" is a good one. In a nutshell, RSS is a mechanism by which your visitors can subscribe to your content (new articles or new blog posts) without having to visit your site and be notified each time new content is posted on your site. We call it subscribing to an RSS feed.
People use an RSS reader to read their feeds, such as Microsoft Outlook for example. Regardless of the news reader that's used, each headline delivered by the feed will appear as an unread email. They aren't really emails, they're just small summaries of each new story with a link to the website.
In short, an RSS feed is nothing more than a list of the latest headlines and excerpts from your site's new stories. Each excerpt contains a link to the full story it refers to. This way, you can draw your visitors back to your website.
So, why should you care? Well, RSS has a lot of marketing value for customer retention. If you can get your visitors to subscribe to your RSS feed, then you can actually publish your content (they call it syndicate) without lifting a finger and reach all your customers for whom your content matters. It's far more effective than if you were to mass-email a newsletter. The difference between a mailing list and an RSS feed is that in the latter, visitors decide to subscribe voluntarily in an unobtrusive way: they can bail out whenever they want.
However, mailing lists have their purpose too: first, you know the size of your target audience (number of emails in list) whereas with RSS it's more difficult (you have to analyze your traffic), and, second, you know your emails reach your entire audience whereas your RSS followers can miss some updates since you only publish the last X recent posts.
But, the single best advantage of RSS is that your content can be "included" by other websites and promoted that way too. You can't do that with a mailing list.