If you are referring to the wires actually at the flash tube, the third wire is the trigger which connects to the trigger transformer.
Originally Posted by Mike Wilde
The transformer gives a very short pulse of very high voltage which ionises the Xenon gas in the tube and starts it conducting.
Unless stopped, the tube will continue conducting until the high voltage capacitor is discharged. A pair of thyristors is used by the light sensing circuit to stop the tube from conducting once enough light is received.