CRI stands for Colour Rendering Index and it measures how closely a light's ability to illuminate an object matches natural/ideal daylight. The higher the CRI rating of a light, the more accurately it renders an object's colour in daylight.
As with many concepts, marketers are generally right in claiming that higher CRI lights do generally renders nicer looking coloration, at least when pertaining to general consumer lighting. However, this does not mean that low CRI lights will produce unattractive lighting.
There is a big difference between colour accuracy and vibrancy (saturation of color tones). With regards to CRI, most folks have the mistaken understanding that a higher CRI means a more accurate color rendition.
What the CRI values measures precisely, is how accurate the color rendition is for a light when compared to a black body radiator of the light's stated K rating value. The Sun is rated at approximately 5780K; stars are near perfect black body radiators so they are good for comparison. If you have a florescent light bulb rated at 5780K, for it to score 100 on the CRI scale, it has to illuminate an object 100% visually similarly to the way our 5780K Sun does.
However, if instead you have a light bulb rated at say 2700K, then for it to score 100 on the CRI scale, it needs to match the illumination standards of a 2700K black body radiator. If we are continuing using stars as an example, this means lighting up an object with a red dwarf star that burns at 2700K, then comparing how visually similarly it is with the light bulb. If the similarity is 100%, then the 2700K bulb will score 100 on the CRI scale.
A light that has 100 CRI while rated at 5780K will illuminate objects hugely differently from a light that has 100 CRI while rated at 2700K. To demonstrate this; remember back in the day when incandescent light bulbs were still used?
A standard incandescent light bulb has a K rating of around 2700k. Incandescent light bulbs are black body radiators, similar to stars. Because of this technical definition, all incandescent light bulbs have 100 CRI by default - yet they render objects in a visually (unattractive) yellowish tone.
To this end, CRI index is not particularly useful for hobbyist aquarium applications. There are many lights that give attractive color renditions and are great for growing plants but may have a low CRI rating. Similarly a high CRI light may actually look visually unappealing; because of the way it is calculated, it has little value for aquarium lighting purposes.
Aquarists are generally more concerned with having vibrant colors with high coloration saturation. Many lights may have a low CRI rating, yet produce very attractive visual coloration; my own LED fixture below only has a CRI of 78, as the overall spectrum is red/blue heavy. However, this allows it to produce more vibrant hues of red and purples. Many others, and myself find the color rendition attractive. Keep this in mind when you are choosing aquarium fixtures.
Choose a light that renders the tank in a fashion that you like. To make the colors pop more in fish and plants, mixing red/blue spectrum in makes a ton of difference. To get a truly accurate sense of color rendition, you do need to see the tank/light in person, and best with side by side comparisons with other light systems.
Head here to learn more about aquarium lighting for planted tanks
Head here to learn more about PAR values.
Head here to learn more about spectrum curves.