The very short version is that Wi-Fi is a way for wireless devices to communicate.
Wi-Fi, short for wireless fidelity, is the Wi-Fi Alliance's name for a wireless standard, or protocol, used for wireless communication. I'll tell you a bit more about this wireless standard and its variations, known collectively as IEEE 802.11, in Chapter 2, “Understanding Wi-Fi.” (IEEE stands for the Institute of Electrical and Electronics Engineers, which defines the standard.)