I'm ignoring output impedance matching and advanced amplifier design and whatnot as that's getting into electrical engineering and physics I don't know. But I do know some stuff about mechanics, so I'll contribute this (and this is for the layperson and my own sanity, so I'm simplifying it. But you can get the picture).
If we look at things in most (maybe pretty much all) cases, audio drivers work better if they are lighter (they can respond faster and more accurately- it's about inertia- That's also why we love electrostatics- which I'm ignoring today). Well, maybe not piezoelectrics and plasma drivers, but let's not go there.
How do we make them lighter? The major moving parts with respect to mass are the cone and electromagnet attached to it (voice coil).
So, as engineers of dynamic headphones, we have made the cone as light as possible by using nano-crystalline membranes grown in distilled baby tears, that are then cryo treated with liquid helium-4 (citation needed). But how do we make the electromagnet lighter? We already are also using nice materials like copper and aluminium and iridium plated dog-hair in the wire, so on we go. There's two major options for lightening this electromagnet:
1: Thinner wires.
2: Fewer turns.
Thin wires have higher electrical resistance. That's why you want them to be thick if you can to drive them easily (to a limit), and why your small desk lamp can have thinner power cables than a vacuum cleaner's.
So let's go all out, screw the ability to drive them easily- we're making expensive stuff so we can anticipate that the customer will be okay with any drawbacks, in the pursuit of quality and perfection, and good reviews on Head-fi.
So, we'll use thin wires. That increases electrical resistance. The Sennheiser HD800 voice coil wires are something on the order of 80 microns in diameter, give or take. That makes for an awful lot of resistance. We could have used thicker wires to reduce resistance and make the headphones easier to drive, but that would be compromise (so we could run them off of an iPod or something). Never compromise when your customer has money!
We can also reduce the length of wire by making fewer loops in the voice coil. We will, however, have to drive more electricity through to get the same magnetic flux as we would with a normal set of headphones- that is, the same amount of magnetism and therefore mechanical power available to move the cone. Fewer turns: we now have less sensitivity, which will demand more voltage out of our amplifier. Again, no compromises!
That's why our desktop amplifiers have to drive something on the order of 15 volts. Cheaper headphones are designed to work with iPods and such, which put out something like 1.2 volts. Those, however, require thicker wires and more turns to drive an equivalent cone. That's a compromise, and this is Head-fi!