Storyboards allow designing the visual layout and flow of an iOS app in Interface Builder. Key features include:
1. Defining view controllers and the transitions between them via segues like push, modal, and custom segues.
2. Configuring properties of view controllers and segues like identifiers that are used to perform segues programmatically.
3. Integrating various iOS components like navigation controllers, tab bars, and container view controllers via segues to define the relationship between screens.