Impedance is the AC resistance of headphones to the audio signal flowing through them, measured in ohms (Ω). A higher impedance requires more voltage to drive the headphones to a given volume. A lower impedance draws more current.
For home studio and mobile use, headphones in the 16–80Ω range are the practical sweet spot. They reach adequate volume from laptop headphone jacks, phone outputs, and audio interface headphone outputs. The Audio-Technica ATH-M50x (38Ω), Sony MDR-7506 (63Ω), and Beyerdynamic DT 770 Pro (80Ω) all fall in this range.
High-impedance headphones (250Ω and above, common in Beyerdynamic and Sennheiser professional models) require dedicated headphone amplifiers to reach proper volume and achieve their full sonic potential. From a laptop headphone jack they may sound thin and quiet.
The relationship between output impedance of the amplifier and input impedance of the headphones also affects frequency response. As a general rule, the headphone's impedance should be at least 8× the output impedance of the amplifier for a flat frequency response.