Why should you display an RSS feed of somebody else's content on your website, other than to be cute and clever? Outbound links don't do anything for your SEO. No, but fresh content does, and that's the beauty of RSS. Google has started putting greater emphasis on fresher content. But what if you don't have the time or inclination to be writing every day? Let others write for you, and get their content via RSS.
An example is a site I run, ossatlanta.org, that tracks the Open Source community around Atlanta. I only update the site with a new story once a month or so. But I have a page on the site talking about every local user group I can find. Under the article is a display of the RSS feed of their upcoming meetings (usually from Meetup.com). So whenever a user group schedules a new meeting, that page on my site's automatically updated. Given the number of user groups and RSS feeds I have, something new appears on the site every day. So when you Google for "open source Atlanta", my site comes up first. Also, on the left sidebar is an RSS feed from my bookmarks that I've tagged with opensource. This counts as fresh content as well.
If you want to see the feed from my bookmarks, click the red "hamburger menu" on the left end of the navbar above.