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.
Step 1: Creating an electron beam
SO, we need a high voltage.