The register function in Strapi allows developers to extend, modify, and inject functionality into the application before it is initialized. It provides a way to dynamically add custom middleware, components, and cron jobs to the application. The Strapi object structure includes various elements such as APIs, plugins, middlewares, policies, services, content types, components, configurations, and cron jobs, providing direct access paths. By leveraging the register function in plugins, developers can create customized functionality without manual configuration. This allows for more flexibility and extensibility in building Strapi applications.