Apple introduced Smart App Banners in iOS 6, which allow app purveyors to present an App Store banner at the top of their websites for visitors on iOS. It's a much less intrusive replacement for those obnoxious, Push-Notification-like "we have an app! Want to see it in the store?" modal dialog boxes that require your input before you can do anything else.
Typically, the banner's button is labeled "View." Tap it, and you'll be taken to the App Store where you can learn more and buy the app. But if you already have the app installed, the label changes to "Open," and tapping it does exactly what you think. This is much like in the App Store itself—if you find an app you already have installed, its label also changes to "Open" instead of displaying a price.