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 only play 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 membrane) 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 mid accentuated and therefore this version is ideal for powerful reproducing of low-frequency material e.g. coming from a bass guitar. The 250 ohms version sounds more smooth and voluminous and can be used for mixing situation within the studio to analyze the whole mix.