Shopify offers two iOS apps, a point of sale (POS) app for the iPad, and this one, an iPhone app to manage your store whilst out and about.
The iPhone app comes with many of the features that you have when logging in to Shopify normally, though not all. You can view a Dashboard, Orders, Products and Customers.
Let's manage some products. You can see I'm selling Lions.
I'm not really, please don't write in.
You can add, edit and delete products as normal.
When customers place an order you can choose to receive push notifications to alert you.
You can see this test order in my test store. I've bought some of those lions. A neat feature is that you can also set up 'One off items' for those special instore situations.
Also, the app has support for signing in to multiple stores at the same time. Neat.