Which component is plugged into the motherboard to allow network connections?

The Network Interface Controller (NIC) Card is the correct component that is plugged into the motherboard to enable network connections. This hardware is essential for a computer to communicate over a network, whether through wired connections (like Ethernet) or wireless connections (like Wi-Fi). The NIC processes the data sent and received between the computer and the network, converting digital data from the computer into a format suitable for transmission on the network.

Having a dedicated NIC enhances the computer's ability to handle network traffic and is crucial for accessing internet services, connecting to local networks, and facilitating data transfer among devices. Other components like the graphics card, power supply, and sound card serve different functions—graphics cards manage video output, power supplies deliver electrical energy to components, and sound cards handle audio processing and output.

Thus, the presence of a NIC is vital for enabling network connectivity, making it the correct answer in this context.