What is fly-by-wire?
The fly-by-wire means that in the aircraft, the (pilot or autopilot) control inputs are fed to the (flight) computer, which processes them and determines the required control surface movements and transmits this by electrical signals (through wires, hence the term fly-by-wire) to the appropriate actuators.

This is in contrast with the mechanical system, where the pilot control inputs are directly transmitted to the flight control actuators, through push-pull rods or cables. The following figure shows the schematic of a mechanical and fly-by-wire system.



Source: euroaviasevilla.es

The first aircraft to use this mode of control was the Avro Arrow, which used a dual-channel fly-by-wire system made of analog circuits. The flight control mechanism on the Apollo Lunar Module was fly-by-wire, the Primary Guidance, Navigation, and Control System, which was referred to as PGNCS, pronounced 'pings'.

Later, NASA tested the fly-by-wire system in a F-8 aircraft, a schematic of which is shown below. Note that it uses Apollo flight computer.



Image from Computers Take Flight- A history of NASA's Pioneering Fly-by-wire Project

In civil aviation Concorde and A320 (which had a digital-fly-by-wire system) introduced fly-by-wire systems, while in military, it was the F-16. At present, almost all combat aircraft and large airliners use fly-by-wire systems.

As an extension, the system is called fly-by-light (or fly-by-optics) is the signals are transmitted through optical cables. If the wires are eliminated altogether, it is called fly-by-wireless.