I've never seriously worked with the storyboard before in Xcode, so here's a summary of what I've gathered so far.
Container view controllers (such as a navigation controller, or a tab bar controller) have a special place in a storyboard, since these container view controllers define how the navigation takes place.
Thinking about the implementation details, I'd expect the storyboard to actually show a graphical representation of an XML file. In this file, the list of screens is saved, including the way how the screens are shown (with animations or what have you). Also present would be the type of container view controller.
In other words, in the MVC-pattern, the storyboard is the input for an over-arcing controller. A big data file, a specification, according to which all container view controllers are instantiated with the correct parameters. Instead of coding, you drag and drop this specification using Interface Builder.
You still have to put in some navigation code, though. Basically you code which segue to perform:
[self performSegueWithIdentifier:@"OfferDetails" sender:self];
If I'd had to put it in one sentence: storyboard replaces the code for navigating between views.