A router manages network traffic by using a routing table to determine where data packets should be sent. In Information Technology networking, a router connects different networks, such as a home local network and the internet, and forwards packets based on destination IP addresses. The routing table contains information about known networks and the best path to reach them. This allows the router to direct traffic efficiently between networks and to serve as a gateway for devices on a local area network. Option A describes a server, which provides services like hosting websites or applications. Option C describes a repeater, which boosts or regenerates signals to extend cable distance. Option D describes a modem, which modulates and demodulates signals to convert between analog and digital forms for transmission over certain media. While modern home routers may also include switch and wireless access point features, the core routing function is traffic management using routing information. Therefore, the correct answer is the option describing maintaining a table and managing traffic, which is option B.