Wikipedia:
The purpose of Wi-Fi is to provide inter-operable wireless access between devices. Wi-Fi generally makes access to information between devices from different manufacturers easier, as it can eliminate some of the physical restraints of wiring which can be especially true for mobile devices
Wi-Fi (IPA: /ˈwaɪfaɪ/) is a trademark of the Wi-Fi Alliance, founded in 1999 as WECA (Wireless Ethernet Compatibility Alliance). The organisation comprises more than 300 companies, whose products are certified by the Wi-Fi Alliance, based on the IEEE 802.11 standards (also called WLAN (Wireless LAN) and Wi-Fi). This certification warrants interoperability between different wireless devices.
The alliance was founded because many products did not correctly implement IEEE 802.11, and some included proprietary extensions. This led to incompatibilities between products from different manufacturers.
The Wi-Fi Alliance tests the wireless components to their own terms of reference. Products that pass become Wi-Fi certified and may carry the Wi-Fi logo. Only products of Wi-Fi Members are tested, as they pay membership and per-item-fees. A missing Wi-Fi logo does not necessarily mean non-compliance with the standard.
In some countries (USA, France, Poland...) the term "Wi-Fi" is often used by the public as a synonym for wireless Internet (W-LAN), although not every wireless Internet product has a Wi-Fi certification. This may be due to certification costs that must be paid for each certified device type.
Wi-Fi certification is provided for technology used in home networks, mobile phones, video games and other devices that require wireless networking. It covers IEEE 802.11 standards including 802.11a, 802.11b, 802.11g, and 802.11n.
Wi-Fi is supported by most personal computer operating systems, many game consoles, laptops, smartphones, printers and other peripherals.