The main function of a router in a computer network is to direct data packets between different networks and manage traffic. Routers analyze the destination IP address of data packets and determine the most efficient path for them to reach their intended destination. They can connect different types of networks, such as local area networks (LANs) and wide area networks (WANs), and may also include firewall features for security. Routers play a crucial role in establishing internet connectivity for devices within a network, making them essential in both home and enterprise setups.