The capacitor is there to save wear and tear on the points, actually.
The magneto gear is attached to an internal magnet which spins inside the primary coil, inducing a current in the coil and producing a magnetic field around it. The magneto is internally timed so that when the magnetic lines of flux are at their greatest, a cam opens the breaker points and causes the magnetic field to collapse. The lines of flux collapse across a secondary coil, which has many turns of wire to step up the voltage. This burst of energy happens exactly when the internal rotor (which is connected to the secondary coil) is lined up with a terminal on the distributor, sending the electricity down the harness to the appropriate spark plug.
The capacitor saves wear on the points and helps facilitate the collapse of the magnetic field. The capacitor is in parallel with the points in the primary circuit of the magneto. When the points just begin to open, the voltage wants to arc across the gap, causing erosion on the points. Since the voltage takes the path of least resistance, it instead flows into the capacitor rather than jumping the gap in the points. By the time the capacitor is charged, the points have opened enough so the electricity can no longer jump the gap.
If you are shutting down the engine and no longer wish for the magneto to fire, you can ground the primary circuit of the magento using a wire. This wire shunts the electricity to ground rather than allowing it to induce a current in the secondary coil. This wire is called the primary lead, or ... wait for it... the P-lead. P-leads carry a surprising amount of electricity, which is why the ignition switches in recip airplanes seem a little bigger physically than you would think is necessary.
At slow engine speeds, like during starting, the magento does not produce enough current to make a good spark. This problem is solved by attaching an impulse coupling to the drive gear of the magneto. The impulse coupling has a little wind-up spring, which will wind itself for about 25 degrees of rotation before letting go and briefly spinning the magneto quickly enough to get a good spark for starting. This also has the desirable side effect of delaying the ignition timing so that the spark occurs around top dead center on the firing cylinder, rather than the normal 20-25 degrees before top dead center we use at higher RPM. After the engine has started, centrifugal pins in the impulse coupling disengage causing it to spin as a unit with the mag and not wind up the spring. If you pull the prop through by hand, that snapping sound you hear is the impulse coupling winding up and releasing. Often only one magneto has an impulse coupling, so the ignition switch grounds the non-impulse mag's p-lead so it won't cause a kickback during starting due to its advanced timing.
Aircraft intended for high-altitude flight often have pressurized magnetos. The lower atmospheric pressure makes it easier for electricity to arc between internal parts of the magento, so they are pressurized using upper-deck pressure from the turbocharger. If you have a turbo airplane that runs rough at altitude, the problem is often a broken magneto pressurization duct and arcing inside the mag.
There's more, but my fingers are tired. Maybe later.