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Networking happens, as most of you might know, when 2 or more computers are interconnected to each other. It is not necessary that the interconnection between computers is through cables as in traditional networking models. With technological advancements, new ways to get connected have come to the fore. These technological advancements include but are not limited to Bluetooth network (with Personal Access Network), Wi-Fi, etc. Following are some self explanatory diagrams of basic networks (note: T stands for a standalone machine or computer).
Direct Cable Connection
Networking With Switch/Hub
Networking With Wireless Router

As you can see wireless networks do not require direct cable connectivity between terminal machines. The communication happens between them through a transmitter that is built in the wireless router device. You can consider it as some sort of antenna. Wireless routers transmit signals which client machines can catch and interpret and act accordingly. However for client machines to be able to catch the signals, they need to have a wireless card. A wireless card helps client machines to send and receive signals to the router. Apart from this mechanism, a wireless router is pretty much same as a normal router. As for security, both routers and client machines need to be configured in advance so that other machines which are not authenticated are disallowed access to the network. Security can also be enhanced by the use of firewall software and encryption mechanisms. If you are deciding to buy a wireless router, I would suggest that you pick from the best available companies like Cisco.