So when people say wireless, what they usually mean is something called WiFi or a wireless network. Also known as a hotspot.
You see these wireless networks everywhere at coffee shops, airports, you can even have one in your own apartment. And basically what it does is kind of take the Internet that you're getting from your Internet service provider and spreads it so that you can use it on every computer you have in your apartment wirelessly, without cables.
It's usually used as something called a router and it creates a radio signal that you can use it with any computer that has a wireless adapter on it. Which means that it can talk to other wireless devices to log into the Internet and shares files and, you know, devices. Like printers, even media to your TV or to your gaming console.
Another important thing to mention is speed. WiFi can be pretty fast but not as fast as connecting your computers to the network with an actual cable. For Internet usage, you won't really see a difference most of the time. But if you're doing more serious stuff like gaming or file sharing, you might want to actually put the cable into the router and connect to your computer manually.
A lot of people ask me how much does having wireless cost. Well the truth is it doesn't really cost anything except for the router itself that transmits the radio signal. In most cases you don't even have to tell your Internet service provider that you have wireless. All you have to do is, go to the store, buy the wireless adapter, plug it into your modem and you're good to go.