An output or jack that carries enough amplification to drive a set of headphones. The key word here is “amplification.” A headphone out should not be routed into a mic-level input. A headphone out will also very likely severely overload (and possibly damage) a line-level input. We’ve seen headphone outputs with watts of output power — enough to drive a speaker cabinet. Use these types of outputs for headphones and speakers, not to route into the inputs of other pieces of gear. Some (not all) headphone outs are designed to handle a wide range of impedances so that they can drive multiple sets of phones simultaneously.
