The device that allows users to share a single internet connection among multiple devices is called a router. Routers manage data traffic between the internet and connected devices, enabling them to communicate over a local area network (LAN). This allows various devices, such as computers, smartphones, and smart home devices, to access the internet simultaneously. Additionally, routers may include features like firewall protection, Wi-Fi connectivity, and network management tools to ensure security and optimize performance for all connected devices.