Colour consistency in an index related to the light sources range of variation in chromaticity (colour) that can be picked up by the human eye.
Why is this an issue for LED?
During the manufacture of LED the colour, luminous flux and forward voltage can all vary. An LED is essentially grown and although accuracy of this has improved over time consistency is still an issue.
How is colour difference measured?
Colour difference is defined by a steps of MacAdamellipse. The scale is set by ANSI Chromaticity Standard. In short though the smaller the ellipse value (size) the smaller the colour difference.