Damping is about the ability of an amp to control the movement of a driver when no signal is send.
Damping factor.
The damping factor of a system refers to the ratio of nominal loudspeaker impedance to the total impedance driving it (amplifier and speaker cable).
As a rule of the thumb, it should be a factor of 8 minimal.
The headphone out of a traditional poweramp is simply the output of the poweramp with a resistor in between to lower the power.
Hence the headphone out has a high impedance by design.
To get sufficient damping, a high impedance headphone is needed.
Typical “classic” headphones like the Sennheiser 600 have a 300 Ohm impedance.
Mobile devices must be frugal on power.
Their small headphone amp struggle to drive high impedance headphone.
This give birth do headphones with a low impedance ( approximately 30 Ohms).
Dedicated headphone amps do have a low impedance output.
More about damping.