Many people use the word.  I suspect not many understand it. 

What is a "flyback" ?  What does "flyback" mean ?

We need to consider the operation of television c.r.ts. 

An electron beam is fired from the cathode at the phosphor/s on the inside of the screen.  The point on the screen at which the beam lands (the 'spot') starts at the top left of the screen, looking at it from the front.  It is swept across the screen from left to right at a steady rate.  When it reaches the right hand edge of the screen it is repositioned at the left hand edge again, a little lower down.  The process continues, the spot being swept across the screen from left to right, repositioned at the left a little further down etc. The left to right sweeps form the lines of the t.v. picture. 

The repositioning of the spot at the left hand side of the screen takes place very rapidly, much more rapidly than the sweep of the spot from left to right.  The spot 'flys back' to the left. 

The movement of the electron beam is controlled by coils round the tube's neck.  There's one set of coils for vertical deflection and another for the horizontal. 

The horizontal coils are driven by the line output stage through a transformer.  The vertical coils are driven similarly but they are irrelevant to this discussion. 

To sweep the spot from left to right a voltage is applied across the coils.  The waveform is basically rectangular.  With a constant voltage across the coils the current through them increases linearly, as does the resultant magnetic field- it's a ramp.  This causes the beam to move linearly across the tube face. 

When the voltage across the coils is removed the magnetic field collapses rapidly. 

This is what happens in a car's ignition system.  Voltage from the car's electrical system is applied across the 'coil'.  The current through it is interrupted by a switch (the 'points' or breaker).  The magnetic field which was created in the coil collapses rapidly.  The 'coil' is, in fact, a high voltage transformer.  The secondary winding has many more turns on it than the primary.  The rapid change in the magnetic field as it collapses induces a high voltage across the secondary.

The same thing happens in a t.v's line ouptut transformer.  It has many more turns than are necessary to drive the deflection coils and it is across these extra turns that a high voltage is developed during 'flyback'.  It is usual for the voltage to be increased further by the use of a series of diodes configured as a multiplier. 

The technique is used not only in t.v. receivers but in other equipment which needs a very high voltage supply.  The transformer at the centre of the technique continues to be called a "flyback" irrespective of the actual application. 

In Britain a line output transformer is called a line output transformer.  The use of "flyback" seems to be peculiarly American.