Application (api) Class
Application class delegates all of the functionality of your applicaiton to Pages, Views, Controllers and Models.
When you are developing your own application you typically would inherit one of Application Classes to make up your own Application object. By default it's located in lib/Frontend.php. This class is instantiated inside your top-most "index.php" file.
In your Application Class you may define more functions which you think should be available from anywhere (such as getCurrentUser()) and perform actions, which you think should always be performed (Such as connecting to DataBase)
You may wonder, why Application class designed for command-line use extends the View. Why application is based on view in the first place?
The reason is because in descendants such as ApiFrontend it's essential that application would have it's own template and be capable of rendering itself. This could have been done through a separate object, but we decided to keep it simple and make it this way.