Digg didn't just redesign their website, they also redesigned their iPhone app. The new app coincides with the recent redesign of the site and adopts the same minimal design the site has.
It'll show you the top stores on Digg right now. It'll also let you share stories to Twitter and Facebook, save articles for offline reading and save articles to reading list apps like Pocket and Instapaper.
A whole new feature which has been introduced is 'Paperboy'. This feature lets you set your home location so whenever you leave home you'll be updated with new articles regularly.