Why three transducers instead of two?

First let's consider the physics of loudspeakers (we also call them transducers or drivers). Transducers can be considered pistons that vibrate room air.

The size of a transducer is directly proportional to the frequency range it's best at creating. If you want to generate low frequencies, you use a big speaker (woofer) - usually 12-, 15-, or 18-inches in diameter; if you want high frequencies, you use a small speaker (such as 1-inch compression driver).

So it follows that there's also an optimum size for a midrange speaker, too (usually 6 to 8 inches in diameter).

A two-way system uses only a high-frequency transducer and a low-frequency transducer (forgive us for stating the obvious) to cover the whole frequency spectrum from the highest highs to the lowest lows (Drawing below). As noted above, size is proportional to output frequency. So in a two-way system, both the HF and LF transducers are being forced to contribute output in a frequency range (mids) that they're not optimally suited to produce.

Worse yet, the transition point when one driver leaves off and the other takes over (the crossover point) is around 2000Hz (see the drawing above). Unfortunately, that's right smack in the middle of the critical midrange frequency band (green area in the drawing). Slight bumps and dips in frequency at the crossover point become very audible.

A three-way system adds a third transducer that's just the right size to produce highly accurate midrange (Drawing above). Crossover points fall at the outer edges of the midrange area (green band). The LF and HF transducers are freed up to produce only the frequencies that they're best at generating 1.