The text details the process of extending an ASP.NET Core web application by integrating user roles and custom claims using FusionAuth. Initially, a group is created, roles are assigned, and users are added to these groups to manage permissions within the application. The discussion progresses to modifying JSON Web Tokens (JWTs) with custom claims, specifically adding a user's favorite color via a lambda function. This lambda, implemented through the FusionAuth API, illustrates the capacity for automation and customization, enhancing the functionality of the application. Finally, the integration allows for personalized user experiences and efficient management of user data, emphasizing the benefits of using FusionAuth for identity management to streamline application development.