Color Rendering is the property of the light source that effects the color of the object. An object looks whitish under the fluorescent lamp and meanwhile, the same object looks yellowish under the incandescent lamp. The same object looks different in(or under?) different light sources. You can see how light source changes the color of objects by comparing under fluorescent lamp, incandescent lamp, daylight and etc. CRI is a numerical representation to evaluate the Color Rendering Properties of the light source.
CRI shows how accurately a sample light source reproduces an object color compare to the reference light source. The CRI value of 100 means the sample light source reproduces the same color as the reference light source does. Therefore the higher the value of CRI is the more resemble to the reference light source.
When evaluating CRI, the reference light source is chosen to have the same (or within the range of 5 mireds) correlated color temperature as the sample light source.