This Ible was written to answer the questions of fellow Ibler, Electorials. I hope it helps.
The flyback circuit is a classic method of generating moderately high voltages. It is not, by any means, the ONLY way, but it was once a very common circuit, and was employed in EVERY CRT based TV or monitor.
It is a VERY clever circuit, because it solves two design problems in the system with one circuit.
The scanning electron beam in a CRT needs to be a.) created and b.) scanned.
All pictures bar two are taken directly from Wikipedia.
The electron beam is created in an "electron gun". A wire filament is heated strongly in a vacuum, and in the presence of a high voltage. Electrons liberated by the heat and voltage are accelerated down the tube and attracted to the screen, where they stop suddenly and cause a phosphor to glow.