Most flashes have an inverter which charges the main capacitor up to a high voltage. This capacitor is permanently connected to the flash tube but the tube will not conduct until it is triggered.
A second small capacitor is also charged up to a high voltage via a large value resistor. It is this small capacitor which is discharged via the sync. contacts into a transformer. The output of the transformer produces a high voltage pulse which triggers the flash tube into conduction.
In simple flash circuits, the whole of the charge in the main capacitor is discharged into the flash tube. Early thyristor flashes used a thyristor to 'short out' the tube when enough light had been delivered. The thyristor bypassed the flash tube and took the remaining charge out of the capacitor.
An improvement of this circuit was to use two thyristors. One was connected between the flash tube and the main capacitor and was effectively held on continuously. The second was used to temporarily switch off the first thyristor when enough light was received. This stopped the tube from conducting and had the advantage of preserving the remaining charge in the capacitor to improve charge time between flashes.