Yeah, basic but looks like still important question! 🙂
Since we human beings can communicate and talk we eager to increase our communication range using innovative solutions.
A really good examples for this is the telegraph wire. Obviously to establish communication and send wired telegraph message to our distant friend we have to setup the medium: wire networks, signal reconditioning stations (repeaters) and telegraph transceiver instruments.
Developing a 4000 mile long wire network is really expensive. So there is a strong demand from the beginning to eliminate the wires. Here comes to the picture the spark-gap transmitter, which uses electromagnetic waves instead of wire networks.
To get back to the initial question: basically wireless is could by any communication device which is not using anymore wires as the communication medium (for practical issues) but rather electromagnetic waves. For example: wifi routers, cellphones, broadcast FM stations, DVB-T TV stations, garage door openers, wireless sensors etc.