Extract from the Beyer Dynamic FAQ
The higher the impedance, the more power is needed to get a proper output volume from the headphone:
32 or 80 ohms = mobile use with laptop, MP3 Player, portable recorder etc..
250 ohms and higher = for permanent installations, headphone amplifiers etc.
Impedance ist the AC resistance of the headphones' voice coil, which is connected to the headphone amplifier. A impedance of 0 ohms would be a short-circuit of the headphone amplifier output; the headphone amplifier supplies an extreme current and after getting very hot, it either turns off automatically - or dies. The other side of the story is infinite resistance (broken cable); no current flows, but also no audio signals arrives - so, we have to be in between these two: 0 and infinite.
In general, headphones with low impedance are designed for use with mobile devices; mobile devices use low power from batteries and therefore also the output power is limited. A low impedance headphone can play (slightly) louder at a low power output. But why high impedance headphones?
The impedance is determined by the voice coil (dynamic headphones), which is a winded copper wire (coated to avoid a short-circuit). This copper wire is available in nearly every length, but not in every gauge (thickness) and a thicker wire has less resistance than a thin wire ("less fits through"). The magnetic field of the voice coil depends on the number of windings of the coil, causing a low impedance system to use a thicker (also heavier) wire and since the membrane foil can't be infinitely light-weight, the moving mass (voice coil and diaphragm) is relatively high. It's pretty clear that a higher mass can't move as easily (following an audio signal) as a lower mass. This low mass can easily be accomplished with thinner (lower weight) wire, but the thinner wire has a higher impedance. This means that the DT 770 PRO with 250 ohms sound more natural, but plays (depending on the used headphone amplifier) not as loud as the 80 ohms version.
The transducers of the 80 ohms versions are stronger and more powerful, a bit more low-mid accentuated and therefore this version is ideal for powerful reproducing of low-frequency material f.e. coming from a bass guitar. The 250 ohms version sounds more smooth and voluminous and can be used for mixing situations within the studio to analyse the whole mix."