The mobile app lets you manage your Google Business information, profile, social shares, analytics, even user access and more via the app. If you manage multiple business, they are all listed there as well, a bit hard to get back to, you need to click the arrow down near the business in the slide out menu.
Here are some screen shots of the app and features:
Mike has a more detailed walkthrough of the app on his blog.
Forum discussion at Google+.