Like other new, high-profile apps (Path comes to mind), Flipboard for the iPhone makes for a fantastic demo. It's what you want to show your mother to explain to her why she should get an iPhone. Its article-to-article and in-story navigation is at once highly unusual and intuitive (you "flip" pages up with your thumb, unlike the iPad version where you flip them to the side). Some of the transitions in the app have subtle effects that make this free app feel lush.
Flip has always been one of the best reader apps, a great app to fire up in a waiting room (or, with the iPhone version, the Starbucks line) to catch up on news and articles. The iPhone version is fast, too, so you won't finish your whole coffee waiting for it to load up (I'm looking at you, New York Times app).
The iPad version is still more attractive, which is not surprising since its extra real estate makes it a much better platform for reading.
Thanks to the Flipboard account feature, your subscriptions on one iDevice are synced to another. I loaded the app up on the iPhone and logged in, and all the sources I had subscribed to on my iPad appeared right away. There's still no Web-based management for Flipboard accounts, though, which I see as an inconvenience. There's also no Android version.
Flipboard CEO Mike McCue has said he's taking the service in a new direction and layering in new socially aware article discovery features. The new version of the app shows where this is going. A "Cover Stories" feed correlates your reading behavior with that of people in your social circles to get you articles it predicts you'll like. As you interact with Cover Stories, it's supposed to get better.
I found, in a very brief test, that Cover Stories did a good job of finding articles I didn't know about and that I would be interested in reading. If, that is, I wasn't already a thousand articles behind in my other feeds--the subscriptions I have signed up for and the non-algorithmic feeds coming from my social connections on Twitter and Facebook.
Several news reader apps (like Zite and News360) are likewise attempting to help readers with "discovery" of content. Flipboard may actually do it better, but I question the emphasis on algorithmic content recommendation. I think this feature is the Groupon of content: fun, sexy, but ultimately not something you rely on, nor is it a feature that builds the customer loyalty that the content providers need.
That said, get this app on your iPhone. Especially if you already use it on the iPad. It really makes short work of powering through your main content feeds, and it looks good and works well enough to vanish into the background as you use it.