Описание тега android-application-class

Extending Android's Application class can be very useful to maintain global state, initialise a module, and so on, before any other part of your code runs.

Android Developer Docs say:

Base class for maintaining global application state. You can provide your own implementation by creating a subclass and specifying the fully-qualified name of this subclass as the "android:name" attribute in your AndroidManifest.xml's <application> tag. The Application class, or your subclass of the Application class, is instantiated before any other class when the process for your application/package is created.