Developing an SMS feedback system with Laravel and Twilio involves several steps, including setting up a new Laravel project, installing the Twilio PHP Helper Library, creating a feedback request form page, handling incoming feedback SMS messages using Twilio webhook functionality, displaying all of the collected feedback, and configuring the application to make it accessible online. The application allows customers to provide their feedback by replying to a feedback request message sent via SMS, and then stores the received feedback in a database for display on a dashboard page.