Impedance and sensitivity are the two specs most likely to be printed on a headphone box and least likely to be understood by the person reading it. Neither number tells you whether headphones sound good. Both tell you something important about whether your existing equipment can actually drive them properly.
Impedance: resistance to electrical current
Impedance, measured in ohms, describes how much a pair of headphones resists the electrical signal being pushed into it. Lower-impedance headphones, typically under 32 ohms, are easy to drive and will play plenty loud from a phone or laptop. Higher-impedance headphones, sometimes reaching several hundred ohms, need more voltage to reach the same volume, which is why they’re common on studio and audiophile headphones designed to be paired with a dedicated amplifier rather than a phone.
Sensitivity: how much sound per unit of power
Sensitivity, usually given in decibels per milliwatt, describes how loud a pair of headphones gets for a given amount of power. It’s easy to assume higher sensitivity is simply better, but very high sensitivity paired with a powerful source can actually introduce audible hiss, since the headphones are efficient enough to amplify a source’s own background noise along with the music.
Impedance asks how hard your source has to work. Sensitivity asks how much it needs to.
How the two numbers actually interact
The two specs work together, not independently — a pair of headphones can be high-impedance but also highly sensitive, in which case they may still play acceptably loud from a phone despite the intimidating ohm rating. The only way to know for certain whether a phone or laptop can properly drive a given pair of headphones is to check both numbers together, or simply listen and check whether the volume feels genuinely maxed out at a level that should be plenty loud.
As a rough rule of thumb worth treating as a starting point rather than a law: headphones under 32 ohms will almost always be fine straight from a phone, headphones between 32 and 150 ohms benefit from a dedicated amp but usually aren’t unlistenable without one, and anything above 150 ohms genuinely needs amplification to sound as intended.