Short for “Wireless Fidelity.” (Yes, it is pretty much a rip-off of the term “Hi-Fi,” or High Fidelity, which refers to high-quality audio or surround sound.) Wi-Fi refers to wireless network components that are based on one of the Wi-Fi Alliance’s 802.11 standards.
The Wi-Fi Alliance created the 802.11 standard so that manufacturers can make wireless products that work with other manufacturers’ equipment. So, if you have a “Wi-Fi Certified” wireless network card, it should be recognized by any “Wi-Fi Certified” access point, and vice-versa. Why there is a Wi-Fi Alliance and why they named the wireless standard 802.11, I am not sure.