The capacitor assists in holding the +coil terminal at a stable voltage. The capacitor charge levels out the peak transients that occur when the ignition coil is charged and discharged to make sparks. To some extent it makes a better spark, and to a greater extent less noise on the 12V supply and radio.
Picture this: The car battery is like a huge capacitor or large water tank, it is charged by the alternator or windmill. The ballast resistor is a small pipe from the large water tank, then the capacitor at the coil is a small water tank that has a faucet at the end that opens and closes for each ignition pulse. If the small tank is large enough to remain full when the faucet is opened and closed, with the pipe (ballast resistor) filling, it the system is stable and the pipes will not pound and make a noise.