dual means the subs has 2 VC's...quad means its has 4. Having more than one VC allows for wiring flexability.
ex: a DVC 2ohm sub can be wired to either 1ohm (parrallel) or 4ohms (series). And a QVC 2ohm sub can be wired to 2ohms (series-parrallel), 8ohms (series), or .5ohm (parrallel).
it's basically how many wires are wrapped (coiled) around the former. these wires are charged and the force produced is combined to oppose that of the magnet, thus moving the piston (cone) forward and backward via respective positive and negative charges. the different number of vc offers different amplifier wiring options.
exactly oso also, chad, remember that the more windings there are the more it will weigh. although lightweight moving masses isnt really the top prority for spl subs, heavy is a bad thing for woofers in general, especially sq woofers.
transient response-how accurate the sub responds to input signals and the subsequent changes in music. typically, the larger the vc, the higher the inductance of the driver, the longer it can contain the current flowing through it before releasing it. this potentially reduces the time it takes to respond to the amp's voltage (resulting in a delayed transient response). it's strictly a function of the current through the driver, not the mass. that's just a myth. its the primary reason i used to always prefer 12"s over 15"s. now i just prefer the "punchyness" that 12"s produce. zac's right. it isn't typically a concern for spl subs. they would rather hold on to as much current as they can. response doesn't matter.