Wi-Fi is "The Standard for Wireless Fidelity."
So what does this mean?
In itself it doesn't mean anything. Wi-Fi is an industry initiative to develop an interoperability test bed for IEEE 802.11b WLAN equipment. This is what enables a card from Lucent to communicate with a wireless access point from Cisco, for example.
The iniative is led by the Wireless Ethernet Compatibility Alliance, or WECA for short. Anybody who wants their product Wi-Fi certified has to become a member of WECA, and can then submit their product to the labs of Agilent. If it passes the required test it gets a Wi-Fi certification and sticker, which to most of us is just a handy way of knowing that it works with other manufacturer's Wi-Fi equipment.
More information about Wi-Fi can be found on http://www.wi-fi.org/ (surprise, surprise).