Whatever you are plugging your headphones into, be it a mobile device, computer, Hi-Fi, TV or a dedicated headphone amplifier, it is important to consider the output impedance of the source, alongside the nominal impedance of the headphones. Impedance is express in ohms (Ω).
If the headphone impedance is too high compared to the output impedance of the amplifier, this may result in a very low-level audio, a lack of volume in the headphones. This is especially evident in mobile devices, where there is simply not enough voltage available to drive a higher impedance headphone.
For this reason, typically, headphones designed for portable devices have a lower impedance of 16Ω to 64Ω (16 ohms to 64 ohms).
If the headphone impedance is lower than the output impedance of the device they are plugged into, this lowers the damping factor, which may result in a significant change from the published frequency response and also cause distortion in the headphones.
Generally, in ear headphones and small portable headphones are low impedance as they are designed to be used with portable devices, so whilst they will usually work with a headphone amplifier, they are not ideally suited to this application and may give disappointing results.
Conversely, some large over the ear headphones are generally designed for Hi-Fi or professional monitoring applications, where the use of a dedicated headphone amplifier will generally offer improvements in the audio quality reproduced by your headphones.
Older HiFi devices in particular often require (much) higher impedance headphones, e.g. 600 ohms.
As a general rule, the output impedance of the device that they are plugged into needs to be lower than or equal to the impedance of the headphones.