I'm not sure I entirely grasp what functionality you're aiming for. I'm not familiar with Buzzfeed.com.
If I understand correctly, you're basically looking to allow users to submit their own content, which would possibly appear on a page on the site, and then have your own content featured on the primary page. Is this correct?
If this is what you're looking for, you can achieve this with a combination of base WordPress functionality and plugins. You can allow registration on the site, force new users to a role that allows them to post their own content, create a category for user created content, and create a page for viewing the content.
You can then use plugins (a rather sizeable list of them, actually) for more refined restriction, like forcing a user to post in a certain category, restricting the capabilities of the user's role, hiding the dashboard capabilities that you don't want them to access, and finally for filtering site admin and user-submitted content to display on the appropriate page(s). (You might also have to make some limited code adjustments within your theme or some of the plugins.)
The end result, hopefully, would be the ability for registered users to submit their own content to display on your site exactly where you want it to display.
If this is not at all what you were looking for, sorry for wasting your time! Otherwise, come up with a good set of keywords and do some searching through the plugin directory and support forums for plugins that do what you need.