An interesting and useful paragraph is the following:
The first function you write for a controller might be the index() function. When a request specifies a controller but not an action, the default CakePHP behavior is to render the index() function of that controller. For example, a request to http://www.example.com/apples/ maps to a call on the index() function of the ApplesController, where as http://www.example.com/apples/view maps to a call on the view() function of the ApplesController.
Notice visibility is also mentioned on the page but starting a function name with an underscore