The function of a router in a network setup is to connect multiple devices, directing data packets between them and managing traffic within the network. Routers act as intermediaries, enabling communication between local networks (e.g., home or office) and the internet. They determine the most efficient paths for data transfer and provide features like firewall protection and NAT (Network Address Translation) for security and resource management. By facilitating both wired and wireless connections, routers are essential for ensuring reliable and efficient network performance, accommodating various devices simultaneously.