Offline functionality is crucial for modern web and mobile applications, especially those with intermittent internet connectivity, and implementing it involves storing application files locally and using local storage as the main data source. This can be accomplished with tools like Progressive Web Apps, Service Workers, PouchDB, and RxDB, syncing data with a remote server-side database such as CouchDB. A tutorial demonstrates building an anonymous chat app using React, Create React App, and RxDB, which functions offline and syncs data once back online. The setup involves configuring the database schema, using RxDB for real-time data updates, and implementing a leader-election algorithm for managing data access across multiple tabs. The app is tested for offline functionality by building and serving a production version that installs a service worker and caches files for offline use, allowing users to continue interacting with the app without an internet connection.