A Wi-Fi network is sometimes referred to as just "Wi-Fi". It is the commercial term for a Wireless Local Area Network (WLAN). The official network protocol is defined by the IEEE 802.11 standard. This network protocol allows mobile devices to communicate on a computer network using radio waves at designated frequencies.
These wireless communications are made possible using a Wireless Access Point (WAP). The WAP device has a radio antenna and a wired connection to a computer network. This wired connection often has access to the Internet and uses the Internet Protocol Suite to communicate.
Please see Wikipedia for more details.