ErstwhileApp is the base class that Erstwhile applications built off of. The bootstrap process creates an instance of your subclass of ErstwhileApp, and then makes it available as a variable called $App.
There are a variety of methods in ErstwhileApp that you can use to access your components, models, etc, and also some others to do things like redirect to other pages, or set up functions for deferred execution after the DOM renders. In addition to these, there are a number of undocumented methods that can be used to change the behavior of your application. These won’t be mentioned here because they may change in the future.