WiFi is a quite straightforward concept really. You pick up a wireless network just like you pick up a radio station - radio waves. A wireless adapter translates data into a radio signal to transmit it via an antenna. A router then receives this signal and decodes it. This information gets form the router to the internet via a wired Ethernet connection.
This can be paralleled with how radio's work. A radio station is like the computer that is translating data (music etc.) to radio waves, and broadcasting these waves a certain radius from the station defining its range. Your radio acts like a router by picking up this signal and decoding it.
What differs between wireless radio waves and other kinds of radio waves like radio stations, cell phones, TVs, etc. is that the frequencies used by WiFi are quite high in comparison allowing these waves to carry a lot more data.