The flyback transformer, or line output transformer (LOPT), is found in any device using a cathode ray tube display, such a televisions, monitors, and oscilloscopes.
The flyback transformer is usually wound on a rectangular ferrite core with a small air gap between the two halves. This air gap is provided as a means of magnetic energy storage, as the flyback transformer behaves more like an inductor than a normal transformer. The windings are located in one or more potted structures mounted on the core.
The name 'flyback' comes from the fact that the voltage in the secondary winding is generated by the magnetic field collapsing while the electron beam "flies back" to the other side of the screen for the next horizontal sweep. The name flyback also quite correctly implies what you will do if you touch the high voltage lead that goes to the CRT anode without discharging it first. See How to safely discharge a CRT before attempting ANY repairs on a television or monitor!
The flyback transformer's basic function is to generate the high voltage needed to fire the electron beam inside a CRT. However, in modern television sets and monitors, additional primary windings allow it to also generate the lower voltages needed for the CRT's filaments (yes, it's got heated cathodes like most other vacuum tubes), the television's tuner, microprocessor, video, and audio circuits. It may serve as the step down transformer in the set's switching power supply, to step down (and up) the incoming 100, 120, or 240 volts DC from the rectifier. The high voltage for the CRT is generated in a seperate secondary winding, which is made of many turns of extremely fine wire. This may be in a seperate potted enclosure from the primary.
Due to the extremely high voltages (up to 50 Kv!) generated by the flyback's secondary, any failure of the insulation causes arcing and carbonization of the epoxy filling, leading to a short circuit in the secondary winding. Thus, flyback transformers are one of the more commonly replaced items during repair of televisions and monitors.