The colour rendering index (CRI) (sometimes called colour rendition index), is a quantitative measure of the ability of a light source to reproduce the colours of various objects faithfully in comparison with an ideal or natural light source.
Light sources with a high CRI are desirable in colour-critical applications such as photography and art.

Most manufacturers use daylight as the benchmark for which to compare colour rendering of lights; daylight is described as the ideal source of illumination for good colour rendering because it displays a great variety of colours, makes it easy to distinguish slight shades of colour, and the colours of objects look natural.

Colour rendering is defined as an effect of an illuminant on the colour appearance of objects by conscious or subconscious comparison with their colour appearance under a reference illuminant – note that the CRI by itself does not indicate what the colour temperature of the reference light source is; therefore, it is customary that the correlated colour temperature (CCT) is also stated.

Basically, what is the difference between the appearance of a colour under a specific light, as opposed to an ideal light source, which is effectively natural daylight. Does the light or lamp make the colour look more blue, or green, or red? Does the colour look flat or is it vibrant and punchy?

It is well known in the lighting industry that the most difficult colour to light is red, which is why this is the real test of LED lighting that claims a high CRI.
We have been involved with lighting many Art Galleries over the years and have, specifically for this application, developed several LED lamps with superb CRI ratings using a custom combination of warm and cold white LEDs.