What is the role of Angular core module?

Your CoreModule contains code that will be used to instantiate your app and load some core functionality.

To get more idea on this read Core Module

Generally Core module is used in order to keep all API services and other common services (like NotificationsService, ConfirmationService, AuthorizationService etc) that you have in your application in the providers[... ] section. Then, the app.module will use your core.module in the imports section.