A featured article is a just a story that will actually get read by people.
Yes I'm being sarcastic but it's pretty true. To view someone's stories you have to click on stories. I never do that and I don't think most users here do. Most don't seem to have any stories anyway. If it's a featured article on the other hand, it shows up around the site and under the articles category. People have a way to find and notice them.
They have to be approved, though. And for good reason: a story can just be a short blurb about your day but an article should at least have some content and be reasonably well thought-out. It should be more like a magazine article than a blog post (in my opinion anyway).
In order for it to be posted as an article, it must go through an approval process by administration. Otherwise it just a story that nobody will ever be able to see except by viewing your profile. Typically its a 24 hour turnaround but can take up to 3 days.
I think it is just one that has been "approved" and it has met standards that will show it as an article that is above and better than many others. It is an article that serves a purpose, tells a story, and educates the reader on real topics that matter to many of us. sometimes you may see articles on the side of the screen those ones are the featured ones, a featured article would receive more views.