JApplet app refers to a reference of JApplet class. This is just a parameter of the method as you see in any other methods. The app variable is similar to the name variable below.
Instead of a String reference, you are passing a JApplet reference as an input argument to the method init() in the SlideShow class.
This method is called from the SlideShowMain class using the code -
So the object that is currently referenced in the SlideShowMain class is passed as the argument to init() method in the SlideShow class. And since SlideShowMain extends JApplet, a JApplet reference can refer to SlideShowMain object.