The computer network in your office is complete collection of computers, printers, cables and other things that are linked together to provide your office with the ability to share printers, the internet, the server and the services it provides.
At the centre of the network usually is a server and a router. The server is a computer that can run software that affects multiple computers, for example file sharing, databases etc.
The router (sometimes call switch or hub) is like a traffic cop that directs digital information around the network to get it to the correct place . It is also the device that connects you to the outside world ie the internet.
When you have the same problem on more than one computer its usually a network problem. When this happens its usually the server or the router that needs to be looked at. (They often just need a reboot.)
As mentioned in other places, if you have IT support, you should consult with them before you make changes to the server or router. And also all other uses should shutdown before you start.
Cabling and wireless
More and more networks are becoming wireless or partly wireless as it becomes more reliable and simple to setup, and .. you can move around. (NB roaming wireless for internet outside your building is something different again. what we are talking about here is wifi)
Cable connections are more stable and faster. But they can get old, broken. Cable is still preferred because of its speed. Wireless because of its convenience.
If you are assessing the overall cost of your hardware, you should include cables themselves and professional installation.
Printing on the network.
The best network printers are those that plug in with a blue internet cable and are setup like any other device on the network.
For offices of less than 30 one network printer is enough. Multiple printers in an office is a sign of dysfunction.
Printer sharing where a printer is plugged into a computer and 'shared' with other users, is to be avoided in an office situation. Possibly ok if you share a second printer that is used for low volume specialist tasks like colour, photos or desktop publishing.
Network printers, that include fax and scanning are becoming more common in CLCs. They can be expensive to purchase but can save money over time due to much lower cost per printed page.
Typically laser printers print at about 1/10th of the cost of (non network) dot matrix/injet (cheaper) printers.