Most turbofans nowadays use "variable stator vanes"; what are these, what is their purpose, and how does it affect a gas turbine's performance?
A fan blade at the front or turbine blade at the back of a jet engine is a small aerofoil surface which is fixed to the main shaft and spins with it. By contrast, a stator vane is a similar aerofoil surface fixed to the outer casing and remains static.
Why do that? The spinning blades of a given stage cause the airflow to start spinning, and that slows the relative speed of the next stage (two things spinning together are at rest with respect to each other). The stator vanes "un-spin" the airflow so that the next stage blades meet it at full speed.
A variable vane pivots about its spanwise (radial) axis, allowing you to change its angle of attack to the oncoming airflow. Why do that? A turbojet engine at different stages in the flight will have different demands and conditions on it and will accordingly spin at different speeds. These effects change the airflow pattern through the engine. If a given stator vane is optimised for one stage of flight, it may not work so well in the modified airflow when a different stage is reached. Varying its angle can ensure that it can always be set at the optimum angle for the best performance.
So variable stator vanes ensure that a given jet engine can always operate at maximum efficiency and deliver optimal performance.
A typical way this is done is to fit gear wheels on the outer ends of the vane pivots, and place a single large toothed wheel around the whole engine so that when the large wheel turns, all the vanes in that position turn with it.