It consists in this case (arrow) of two rolled up layers of foil with isolating interlayer and is switched in parallel with the contact-breaker points. While opening the contact-breaker points it takes up the loads which develop from the self-induction of the primary part of the ignition coil.
It is typical for coils that a tension is induced by their magnetic field even after the electric power is taken off again. If the capacitor takes this up, it helps to reduce the magnetic field fastly and provides with it for stronger sparks. A resonant circuit develops, disconnected from the remaining electric components, between primary winding and condenser.
Without capacitor the open contact-breaker points would be hit by tension with sparking, causing damages. The high voltage is decisively reduced. Ignition time and dwell angle would alter. The engine is not operable without condenser. 06/09