The Box API uses OAuth2 for authentication. Since OAuth is a little tricky, the SDK provides an OAuth WebView UI using JavaFX. This WebView must be built separately because it has an extra dependency on the JavaFX JDK.
JavaFX is included by default starting with JDK 7u6. You can find more information about it here. There is also a JavaFX Eclipse plugin if you're using Eclipse as your IDE.
You can find a sample here. One thing to pay extra attention to is that the callbacks in the IAuthFlowListener must use SwingUtilities.invokeLater(runnable) when interacting with the UI.