When the points are closed, a magnetic field is built up in the core of the coil. When the points open, the field collapses, and induces a sharp voltage rise in all of the windings, both primary and secondary. That means the voltage across the points tries to shoot up to several hundred volts. Not a problem if they are fully open, but they actually open pretty slowly (especially when just cranking the engine). Without the condenser, the rising voltage jumps the tiny gap at the points, and dissipates most of the energy stored in the coil, leaving none to jump the plug gap.
Oh, and the voltage still rings after the spark is over. Doesn't matter at all, because it will stop when the points close and short out any ringing still going on.