Slim is a lightweight PHP micro-framework that provides compatibility with various PSR standards, including PSR-11 for the container, PSR-7 for HTTP messages, and PSR-15 for middleware. To add Twig as a view renderer to Slim, Composer is used to install Twig, and a configuration file is created in the `config/dependencies.php` directory to tell PHP-DI how to create a new instance of the Twig environment when requested. The Twig environment is then available in the handler, allowing it to render templates using the `render` method. A template named "home-page.twig" is created in the `view` folder and contains placeholders for variables that are passed to it from the handler. With this setup, Slim can now use Twig to generate HTML responses.