The 2 transformers represent a single step-up transformer with a center tapped primary. The diodes at the transistor shunt excess drive current to the collector and prevent negative spikes from damaging the transistor.
Circuits like this are commonly used in the first stage of camera flash circuits and in handheld "bug zappers". Typically the storage capacitor would be between 680nF and 330uF but I reduced the value to speed up the simulation.
