fly back inverter is such kind of DC-AC inverters which use the flyback transformer for the low dc-high dc stage of the inveter

shortly it's DC to AC inverter with flyback transformer inside .

you touch both of it's high voltage outputs together.

its a line output transformer, also known as a flyback transformer, it provides the high votage required to run the tube. http://en.wikipedia.org/wiki/Flyback_transformer

In most sets, the HV regulator actually regulates the B+ voltage to the horizontal output transistor and the flyback transformer. A bad regulator indicates high current or loss of horizontal drive. Check the flyback transformer, the HO transistor and also look for proper waveform and voltage from the horizontal driver transistor/chip.

A type of high voltage transformer. Their most common use was in CRT based TVs & computer monitors to generate the anode high voltage and horizontal sweeps.