Lightness is a visual perception of the luminance of an object. It is often judged relative to a similarly lit object. In colorimetry and color appearance models, lightness is a prediction of how an illuminated color will appear to a standard observer. While luminance is a linear measurement of light, lightness is a linear prediction of the human perception of that light.
This distinction is meaningful because human vision's lightness perception is non-linear relative to light. Doubling the quantity of light does not result in a doubling in perceived lightness, only a modest increase.