The CDI method is simply more efficient at giving you a spark, or a multi-spark in more advanced systems. The excitor acts like a pre-charger for the capacitor, building up a voltage much higher than the 12 volt battery alone, so the ignition coil can be much smaller than in the past. In the case of CDI the ignition coil is pulsed, not charged up, thus saving time and wasted energy.
The intense pulse of current only occurs by a trigger that is connected to your timing belt/chain, so that it fires the spark plug at just the right instant, discharging the capacitor.
The old fashioned way was to close the 'points', charging up the coil, then open the points and let the bypass cap cause the plug to spark. The CDI way removes this long coil 'ON' time which waste power, and is more difficult to get the tach and dwell set correctly.
In the CDI version the excitor is always running when your engine is running, keeping the capacitor charged up (it happens real fast), so it is ready to use. The better ignition systems have a coil per each plug, using a common exciter to supply a high pre-charge voltage in which the firing of the plug is under computer control.
This results in much better fuel efficiency and spark-plug life due to the firing computer making fine adjustments to firing times and fuel/air mix.
There are much fewer turns of wire on the ignition transformer secondary. With only 12 volts, the input/output voltage ratio was at least 5000:1. If you drive the new ignition coils with 600 volt pulses (from the excitor), your turn ratio is only 40:1, so your ignition coil is much smaller and fires faster. Taser guns are made this way - A 2 step process to get the 50,000 volts at the output pins.
I found a snippet from an article on some of the details of CDI Ignition systems. The source is: https://en.wikipedia.org/wiki/Capacitor_discharge_ignition
Typical CDI module
A typical CDI module consists of a small transformer, a charging
circuit, a triggering circuit and a main capacitor. First, the system
voltage is raised up to 250 to 600 volts by a power supply inside the
CDI module. Then, the electric current flows to the charging circuit
and charges the capacitor. The rectifier inside the charging circuit
prevents capacitor discharge before the moment of ignition. When the
triggering circuit receives the triggering signal, the triggering
circuit stops the operation of the charging circuit, allowing the
capacitor to discharge its output rapidly to the low inductance
ignition coil. In a CD ignition, the ignition coil acts as a pulse
transformer rather than an energy storage medium as it does in an
inductive system. The voltage output to the spark plugs is highly
dependent on the design of the CD ignition. Voltages exceeding the
insulation capabilities of existing ignition components can lead to
early failure of those components. Most CD ignitions are made to give
very high output voltages but this is not always beneficial. When
there is no triggering signal the charging circuit is re-connected to
charge the capacitor.
The amount of energy the CDI system can store for the generation of a
spark is dependent on the voltage and capacitance of the capacitors
used, but usually it is around 50 mJ, or more. The standard
points/coil/distributor ignition, more properly called the inductive
discharge ignition system or Kettering ignition system, produces 25mJ
at low speed and drops off quickly as speed increases.
One factor often not taken into consideration when discussing CDI
spark energy is the actual energy provided to the spark gap versus the
energy applied to the primary side of the coil. As a simple example, a
typical ignition coil may have a secondary winding resistance of 4000
ohms and a secondary current of 400 milliamperes. Once a spark has
struck, the voltage across the spark gap in a running engine drops to
a relatively low value, in the order of 1500-2000 volts. This,
combined with the fact that the coil secondary current of 400
milliamperes loses approximately 1600 volts through the 4000 ohm
secondary resistance means that fully 50% of the energy is lost in
heating the coil secondary. Actual measurements show the real world
efficiency to be only 35 to 38% when coil primary winding losses are