Here is the technical description of the operation of the circuit:
When the supply is connected, both transistors are off and the electrolytic charges via the 330k resistor and 22R. When the voltage on the base of Q1 rises to about .6v, the transistor begins to turn on and the resistance between its collector-emitter terminals is reduced. This allows current to flow in the collector-emitter circuit and Q2 is turned on via the 1k resistor. The 10n reduces the effect (the resistance) of the 1k resistor. Q2 conducts and the LED is illuminated. The current through the LED is limited by the 22R resistor and at this point in the cycle a voltage is developed across the 22R. The negative end of the electrolytic is `jacked up' by this voltage and the positive end pushes the charge on the electrolytic into the base of Q1 to turn it on even harder. In a very short time all the energy in the electrolytic has been delivered to Q1 and it cannot hold Q1 ON any longer. The transistor turns off slightly and this has the effect of turning off Q2 a small amount. The LED begins to turn off and the voltage across the 22R reduces. The negative lead of the electro drops a small amount and so does the positive lead. This action continues around the circuit until Q1 is fully turned off. This turns off Q2 and the LED is extinguished. The cycle starts again by the 10u charging. The charge-time is considerably longer than the discharge time and this gives the LED a very brief flash.