Wi-Fi is a trademark of the Wi-Fi Alliance. It can be used with certified products that belong to a class of wireless LAN, local area network, (WLAN) devices based on the IEEE 802.11 standards.
The wireless part of Wi-Fi refers to a low power transceiver using an unlicensed band of frequencies around 2.4 GHz. It competes with other wireless technologies in this space such as Bluetooth and your microwave oven. Since 2009 Wi-Fi has also been available on the 5.0 GHz band with much less interference.
A transceiver is located in your portable device and communicates wirelessly with a router which channels the information into a wired internet connection. It is mainly used in business, homes, and some commercial establishments like coffee shops and book stores. In the later case these places are called hotspots as they allow an internet connection for all devices that are nearby. The connection may or may not be free of charge. Business and Home use is typically password protection to avoid use by unauthorized people and to provide security for the connection.
 IEEE 802.11
IEEE 802.11 is a set of standards that apply to wireless local area network (WLAN) computer communication in the 2.4, 3.6 and 5 GHz frequency bands. It uses techniques of spread spectrum and/or frequency division multiplexing to provide good local communication with low power devices. It defines both the hardware capabilities and the protocol to be used. It is subdivided into 3 groups based on the speed of the transmission for the 2.4 GHz band. (Other letters are used for additional capabilities, frequencies, and needs)
- b - Is the slowest form currently in use. It has a maximum raw data rate of 11 Mbit/s. When it arrived in the year 2000 it was faster than previous methods and quickly adopted as the baseline. Channel width is 22 MHz
- g - It appeared in June 2003 and operates at a maximum physical layer bit rate of 54 Mbit/s exclusive of error correction codes, or about 22 Mbit/s average throughput. 802.11g hardware is fully backwards compatible with 802.11 b hardware but the protocol is different. Channel width is 22 MHz.
- n - It first appeared in 2007 and was adopted in 2009. It is designed to improve network throughput over previous standards, such as 802.11b and 802.11g, with a significant increase in the maximum raw data rate from 54 Mbit/s to a maximum of 600 Mbit/s with the use of four spatial streams at a channel width of 40 MHz. Less streams and/or less channel width provides less speed improvement. The n group can also use 5.0 Ghz band. It can also use Multiple Input Multiple Output (MIMO) technology, which uses several antennas to send and receive up to four spatial streams, resulting in enhanced performance.
- ac - The latest and fastest Wi-Fi connection with 3X performance over the existing n service at up to 1750 Mbit/s.
The speeds mentioned are theoretical maximums are are decreased by distance from the router and competition with other Wi-Fi users and nearby competing technologies in the frequency space.
 WiFi Direct
WiFi Direct applies the Wi-Fi technology to allow point to point communication between two Wi-Fi enabled devices. It differs from regular Wi-Fi in that it doesn't need a router and is intended to allow device to device communication between devices that are not from the same manufacturer. It overlaps, to some degree, the capabilities of Bluetooth but is capable of a faster data rate.
 WiFi Hotspot
A WiFi hotspot is a device that can serve as the central router for a network. A standard router can be a WiFi Hotspot but the term usually refers to a device such as a cell phone that provides the service using a cellular network. A Hotspot generally provides a connection to the Internet for all wireless connected devices but may also be used to provide a local network capability for these connected devices. For example a separate storage device may be able to stream movies or even eBooks to a local network of devices in a car while it is driving down the road. In this case it is behaving like a local cloud server.
The term WiFi Hotspot can also be a reference to a public location, such as a restaurant or coffee shop, that provides an Internet connection for WiFi enabled devices.