The very short version is that Wi-Fi is a way for wireless devices to communicate.
Wi-Fi 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, later in this chapter. (IEEE stands for the Institute of Electrical and Electronics Engineers, which defines the standard.)
The Wi-Fi Alliance
The Wi-Fi Alliance is a not-for-profit organization that certifies the interoperability of wireless devices built around the 802.11 standard. The goals of the Wi-Fi Alliance are to promote interoperability of devices based on 802.11 and, presumably, to promote and enhance the standard.