Chairs that move on their own are composed of individual robotic modules, each equipped with a microprocessor, power source, and actuators. These modules communicate through connectors that allow them to twist and collaborate to achieve movement. The technology behind these chairs is highlighted in articles from Gizmag and How Stuff Works, showcasing various innovative robots. Additionally, there are designs for chairs that can collapse and self-repair, demonstrating advanced engineering. Overall, the discussion emphasizes the ingenuity of robotic chair technology and its potential applications.