Impedance: Is measured in Ohm (Ω) and tells you how hard a headphone’s driver actually hinders the flow of electrical current in the voice coil. The fine wires in the voice coil resist the electrical signal and said “impedance” must be overcome by the power output of the amplifier. If the amplifier cannot push enough power, insufficient volume and clipping dynamic peaks will be the result.
Efficiency: has to do with energy transfer. I put this many (Milli)-Watts in, I get this much sound pressure (aka. volume) out. A low efficiency load will consume a relatively large amount of power (energy) to produce a certain Sound Pressure Level (SPL). Naturally, the lower the efficiency rating of a headphone, the harder it is to power. Demanding headphones with high impedance and low sensitivity will require additional hardware in the form of a headphone amplifier to work correctly
Headphone manufacturers use two different ways of reporting the efficiency or sensitivity of headphones:
To exactly calculate how loud your amplifier can drive your headphones you need to know its voltage (Vrms value).
Depending on what specifications you are able to find on a headphone's product page, you can apply the following:
32 Ohm and 99dB/mW or more: You don’t need an amplifier: This headphones can be easily used with battery powered mobile devices (smartphones, tablets).
32-80 Ohm and 96dB/mW or more: Can be used with a high quality desktop computer, laptop or portable smart-device. Low quality devices may already struggle to reach enjoyable listening levels with quiet songs.
32-80 Ohm and less than 96dB/mW: You should invest in a competent headphone amplifier. Low efficiency and low impedance implies above average current draw.
80-300+ Ohm and less than 99dB/mW, : You should definitely get a competent headphone amplifier.
Please keep in mind that this was a simplified explanation and if you are interested in the topic of amplification please take the time to read the following two articles: