When the circuit is powered up a certain current flow from the base of transistor BC558 into the 560 k? resistor. At the same time the transistor itself goes into conduction and through a resistor of 1.8 k? a certain current reaches the base of transistor BC548/547 so that it also goes into conduction.
Now the electrolytic capacitor is charged through the base of the transistor BC558 and this current passage makes the transistor more conductive and so the light bulb lights up.
As soon as the capacitor is charged, the base current of the BC558 is not sufficient to maintain the transistor itself at the conduction state. Therefore, the current to the base of transistor BC548/547 is interrupted.
The bulb goes off, the collector voltage rises to 4.5 volts. At first the capacitor remains unchanged and the voltage at the base of the BC558 rises to 7.4 volts. But through the 560 kOhm resistance the capacitor is discharged again and the voltage at the base of the BC 558 drops again to the value of 3.8 V.
In this way the cycle repeats itself.