As the other replies have said, you have a wired LAN in your property - whether it works is another matter, but it should be very straightforward to configure and find out.
The dual sockets are the network modules into which you can plug an RJ45 Cat5 network patch cable and then connect the other end of the cable into a PC's wired network port (also RJ45). The network points are numbered to match the patch panel ports, so assuming your router has more than one RJ45 socket for wired networking, you can connect a PC to say, network module 1, then at the patch panel end, connect port 1 to one of the wired ports on the router. Do the same for each of the wired network connections to a PC, until you run out of PCs and network ports at the router.
Your PC should indicate what type of wired network connection in the network connection status window. If you're using Cat5e patch cables and the network is wired with Cat5e cable, then you'd normally get gigabit ethernet, but given that your router probably has 4 fast ethernet ports, it'll be 100Mbps ethernet, which is still way faster than wireless.