cielab is industry terminology for a way to describe colour.
cielab is a 3D XYZ axis that scientifically describes how the average human eye sees colour proposed by the CIE (Commission Internationale de I’Éclairage). L, A & B are the three axis that place the colour in this 3D space. Any colour conversion needs a universal middle way to convert the colour. As an example, if viewing a CMYK file on an RGB monitor you are actually using 2 ICC profiles even if you don’t realise it or aren’t controlling it. But CMYK has absolutely no relationship to RGB, so these 2 ICC profiles (RGB & CMYK) go into cielab as a way to calculate this conversion.
Example of how the conversion works:
|File Being Edited||Output on Monitor|