Phil Belanger, a founding member of the Wi-Fi Alliance who presided over the selection of the name "Wi-Fi" writes:
Wi-Fi doesn't stand for anything.
It is not an acronym. There is no meaning.
Wi-Fi and the ying 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". Interbrand created "Prozac", "Compaq" "oneworld", "Imation" and many other brand names that you have heard of. They even created the company name "Vivato".
The only reason that you hear anything about "Wireless Fidelity" is some of my colleagues in the group were afraid. They didn't understand branding or marketing. They could not imagine using the name "Wi-Fi" without having some sort of literal explanation. So we compromised and agreed to include the tag line "The Standard for Wireless Fidelity" along with the name. This was a mistake and only served to confuse people and dilute the brand. For the first year or so( circa 2000) , this would appear in all of our communications. I still have a hat and a couple of golf shirts with the tag line. Later, when Wi-Fi was becoming more successful and we got some marketing and business people from larger companies on the board, the alliance dropped the tag-line.
This tag line was invented after the fact. After we chose the name Wi-Fi from a list of 10 names that Interbrand proposed. The tag line was invented by the initial six member board and it does not mean anything either. If you decompose the tag line, it falls apart very quickly. "The Standard"? The Wi-Fi Alliance has always been very careful to stay out of inventing standards. The standard of interest is IEEE 802.11. The Wi-Fi Alliance focuses on interoperability certification and branding. It does not invent standards. It does not compete with IEEE. It complements their efforts. So Wi-Fi could never be a standard. And "Wireless Fidelity" - what does that mean? Nothing. It was a clumsy attempt to come up with two words that matched Wi and Fi. That's it.
So we were smart to hire Interbrand to come up with the name and logo. We were dumb to confuse and water down their efforts by adding the meaningless tag line. Please help reinforce the good work that we did and forget the tag line.
I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.