A flyback transformer also called a line output transformer (LOPT), is a special transformer

Transformer

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...

, which is used for conversion of energy (current and voltage) in electronic circuits. It was initially designed to generate high current sawtooth signals at a relatively high frequency. In modern applications is used extensively in switched-mode power supplies

Switched-mode power supply

A switched-mode power supply is an electronic power supply that incorporates a switching regulator in order to be highly efficient in the conversion of electrical power...

 for both low (3V) and high voltage (over 10 kV) supplies.

It was invented as a means to control the horizontal movement of the electron beam in a cathode ray tube

Cathode ray tube

The cathode ray tube is a vacuum tube containing an electron gun and a fluorescent screen used to view images. It has a means to accelerate and deflect the electron beam onto the fluorescent screen to create the images. The image may represent electrical waveforms , pictures , radar targets and...

 (CRT).