WiFi at one time meant wireless fidelity, analogous to HiFi. WiFi is the term for a Wireless Local Area Network, specifically 802.11 compliant. WiFi allows computers to wirelessly access other computers and printers, and typically it allows Internet access. So if you have a laptop, or an iPad, you can go into a library or coffee shop that has WiFi, join the network, and have Internet access.
Another term that may be used is Wireless-g or Wireless-n. Wireless-g is fast enough for video. Wireless-n (802.11n) is even faster, and it will support wireless-g devices also.