Despite the similarity between the terms "Wi-Fi" and "Hi-Fi", statements reportedly  made by Phil Belanger of the Wi-Fi Alliance contradict the popular conclusion that "Wi-Fi" stands for "Wireless Fidelity".
According to Mr. Belanger, the Interbrand Corporation developed the brand "Wi-Fi" for the Wi-Fi Alliance to use to describe WLAN products that are based on the IEEE 802.11 standards. In Mr. Belanger's words, "Wi-Fi and the yin yang style logo were invented by Interbrand. We (the founding members of the Wireless Ethernet Compatibility Alliance, now called the Wi-Fi Alliance) hired Interbrand to come up with the name and logo that we could use for our interoperability seal and marketing efforts. We needed something that was a little catchier than 'IEEE 802.11b Direct Sequence'."
The Wi-Fi Alliance themselves invoked the term "Wireless Fidelity" with the marketing of a tag line, "The Standard for Wireless Fidelity," but later removed the tag from their marketing. The Wi-Fi Alliance now seems to discourage propagation of the notion that "Wi-Fi" stands for "Wireless Fidelity" but includes it in their knowledge base:
To understand the value of Wi-Fi Certification, you need to know that Wi-Fi is short for "Wireless Fidelity," and it is the popular name for 802.11-based technologies that have passed Wi-FI certification testing. This includes IEEE 802.11a, 802.11b, 802.11g and upcoming 802.11 technologies.