Fly by wire is not directly the reason for the Airbus 'sidestick', as the 777 (with a conventional control column) is also fly-by wire.
It is the future of aircraft design, and no new aircraft design of the future will even not be fly-by-wire until a replacement is found for it.
As simply as possible, Fly by wire is a different way of commanding flight controls on an airliner. The flight controls are, of course, still moved by hydraulic power as they have been for many years, but in a fly-by-wire aircraft the signals are sent to the hydraulic jacks and actuators on the control surfaces electronically, rather than mechanically. This has saved the use of heavy mechanical rods, levers and springs which were previously used, replaced with wires which results in large weight savings for aircraft which makes them more efficient.
Also with fly-by-wire, no physical effort is required to move the controls, so a sidestick was introduced by Airbus giving the pilot an uncluttered view of the instruments, allowing the instruments to be larger, and also allowing us to have lunch in comfort at last!
That was, of course, a simple explanation of how it works, the electrical signals actually pass through an array of computers which transmit further electrical signals to the control surfaces, and it is all fairly techincal, much more than I know at least. Nevertheless I hope you are a little clearer as to the controls which will be present on new aircraft in years and decades to come.