Impedance is expressed in Ohm.
Often it is mistaken for resistance as resistance is also expressed in Ohm.
Resistance (Ohm's law) is DC resistance.
Impedance is the resistance when an alternating current is used. Basically, it is frequency dependent.
A simple example is an analog interconnect and a digital interconnect like a 75 Ohm SPDIF cable.
If you measure resistance using a multi meter, both will have the same value pretty close to zero. If you send a signal with a high frequency over the cablse a true SPDIF cable will have a 75 Ohm impedance and any other coax cable will have some value but most of the time not 75.
Headphones have an impedance.
Classic designs do have a high impedance.
In the past the headphone out of a (power) amp was a matter of connecting the headphone to the same output as the speakers. This of course will fry the headphone. To avoid this, a resistor is used to lower the power. Nothing wrong with this approach but the result is an amp with a high output impedance.
A rule of the thump is that the damping factor, the impedance of the headphone divided by the impedance of the amp, should be 8 as a minimum. Often this value is criticized as being to low.
Driving high impedance headphones is no problem for a desktop amplifier or a dedicated headphone amplifier. Enough power to do that. Cell phones, however, don't have big amps and like anything that conserves battery power.
This gave birth to a whole new type of headphone, the impedance is very low, often 32 Ohm or less.
They can be driven by a couple of milli watts hence by any mobile.
More about damping.
It looks simple, high impedance headphones for powerful stationary gear and amps with a high output impedance (valves!) and low impedance for portable use.
Practice is more complex.
There are headphones with high impedance that are easy to drive and low impedance headphone that are hard to drive. This is called sensitivity.
It is the amount of power needed to reach a certain level of loudness.