|I am wondering what the cable wires or sockets on the back of this router are for? |
This is impossible to answer without knowing the make/model of the router. If it's an enterprise level Cisco router, you could be looking at a console port or a network interface.
If it's a SOHO Router, then you connect the network patch cable from your cablemodem into the WAN port of the SOHO Router. Clients get plugged into the LAN port(s).
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.