What is a C.D.I. (Capacitive Discharge Ignition)

A CDI is an electronic type of ignition circuit. The basic concept is the same with conventional ignition circuits. A switch cuts the current through the primary coil of a transformer when the spark plug needs high voltage to make spark. The secondary is directly connected to the plug (in TA, at least two transformers needed). In the old conventional systems (not used anymore), the switching was accomplished by a mechanically driven circuit breaker. That breaker was switched on-off exactly as many times (per revolution) a spark is needed. In "transistorized" electronic ignitions, this breaker has been replaced by a transistor. A suitable sensor (of magnetic type) drives the transistor circuit, thus mechanical switch is gone (it's unreliable operation, too)
and the switching frequency can be much higher (as in high efficiency multi-cylinder motors) without reducing spark energy.

Current through the primary coil is not drawn anymore when engine is not running, and special circuitry provides an ignition "map" ie a means of varying the ignition advance (?) vs RPM. This map is not neccessarily linear, as it was in the conventional systems where a centrifugal mechanism was used. Additionally, in TA96 and above, a throttle position sensor sends additional information to the ignition, although I do not know in which way it affects advance. I suppose it acts like the vacuum valve in the older car ignition systems (improves efficiency at heavy loads). Does anybody knows further details ?

Electronic ignitions have many other advantages, including better operation in cold weather, where battery capacity is lower. This is accomplished by the current limiter (it supplies the constant current to the coil independently of battery voltage).

A CDI unit is a further improvement in which a capacitor is charged and then supplies current to the coil. Just because the capacitor can supply very high peak current (much higher than the battery-switches-fuses-cabling combination), output voltage is higher.

There are only two disadvantages of the electronic ignition circuits:
a) Their semiconductors are suceptible to damage due to the high voltages, thus a very careful design is needed (that's why sometimes the first production of a new model has ignition reliability problems). 
b) PCB board and the components themselves are subject to vibrations and other mechanical strains. This is the reason that early TA CDIs fail (they were badly fiitted under and very close to the saddle).

I hope I didn't confuse you too much (I thought all the above might be useful to those who want to have a better understanding of the ignition circuit).