Basic physics.
Voltage is analogous to water pressure through a hose and current is analogous to water volume through a hose. You may have water flow through a hose nozzle with your finger plugging the end (high impedance), creating more pressure (voltage), but actually less volume of water (power) is flowing through. A fully open hose nozzle (low impedance) allows more water (power) through, though with less pressure (voltage). The two are inversely related.
So for high impedance headphones if you don't push enough voltage (higher volume setting) you won't get good control of the transducer for a given sensitivity rating, but it doesn't suck up as much power. For low impedance headphones the voltage requirement is lower (lower volume setting) but there is less resistance to the power flow so it sucks the juice faster for the same sensitivity rating. In simple terms.
In summary:
Higher impedance (high resistance to flow) requires more voltage but it sips the power. Lower impedance (low resistance to flow) requires more current and gobbles up the power.