The primary purpose of a router in a computer network is to direct data packets between different networks and devices. Routers facilitate communication by determining the most efficient path for data transmission, allowing devices within a local area network (LAN) to connect to the internet or other networks. They also provide features such as firewall protection, network address translation (NAT), and sometimes DHCP services. By managing traffic and ensuring secure data transmission, routers play a critical role in maintaining efficient and reliable network performance for both home and enterprise environments.