This write-up is one of the best I've found explaining how the condensor (capacitor) works in a Kettering points system. I think of them as temporary voltage storage units from a mechaical engineer's perspective

. For kick-start motorcycles, the alternator stores charge in a large capacitor. There is then enough voltage and amperage to start the bike.
"And somewhere around the time of 04/16/2004 09:10, the world stopped and listened as
Don Bruder contributed the following to humanity: Actually, it's both. The condenser(capacitor) is about .22uf give or take for design differences. I don't know what the mH rating of a coil is, but the coil is a electrical device known as a auto-transformer. It's like a regular transformer, but both the primary and secondary share some of the windings.
The capacitor is wired in parallel to the points and in series to the coil.
The capacitor tries to maintain a constant voltage while the coil tries to maintain a constant current. The basic design of a automotive ignition circuit is basically a series resonance circuit not unlike those used in radio.
When the points are closed, the capacitor is shorted out and current flows from ground, through the points, through the coil, and out onto the positive power rail. This sets up a magnetic field around the windings of the coil. At the moment that a spark plug is to fire, the points open which interrupts the current flowing through the coil, but the coil is charged (magnetic field), and
in an attempt to keep the current going, the coil discharges right into the capacitor.
At this point, when the coil is fully discharged, there is a voltage charge on the capacitor in the range of +700-1000 volts in reference to ground. Since this is much higher than the +12V rail that the other end of the coil is connected to,
the current flows BACKWARDS from +12V, through the coil, and into the capacitor to even the charge. Because there is little resistance in the coil, a high amperage pulse is generated through the coil primary, and with a winding ratio of 40:1, causes a voltage spike between 28KV and 40KV on the secondary, which is more than enough to jump the gap between the rotor and distributor cap, and the gap on the plug itself.
A leaking capacitor will dissipate some of the charge before it can be used to draw the current through the coil resulting in a lowered high voltage output and a weak, or no spark condition.
A shorted capacitor will cause a no-spark condition because the current will still flow through the coil.
An open capacitor will burn the points because the points will be forced to absorb the discharge from the coil causing them to arc, and you will get a weak or no spark.
Too little capacitance will cause the points to burn too, the same reason that a open capacitor will. But, it may or may not cause a weak/no spark condition depending on how much under the spec the cap is.
Too much capacitence will cause a weak or no spark condition because the voltage across the capacitor will not be high enough because of the larger value. The bigger the cap is, the bigger the charge on the coil has to be to get it to the 700-1000 volt range.
Generally the bad condenser will cause the contact points to burn
*unless* the condenser itself develops an internal short. Then it will ground the primary current from the coil
*permanently* hence no interruption of the coil primary current flow resulting in no high voltage (spark) generation in the secondary circuit"