The Color Temperature of a light source defines its "whiteness", its yellowness or blueness, its warmth or coolness. It does not define how natural or unnatural the colors of objects will appear when lighted by the source. Two colors of lamps can have the same Color Temperature, but render colors very differently. For example, the SP30 and SPX30 fluorescent lamp colors have about the same color temperature as do high wattage incandescent lamps, but they have far less red energy in their spectrum. Therefore, red colors will not appear as bright under SP30 and SPX30 as they would under incandescent.
Color Rendering IndexTo help indicate how colors will appear under different light sources, a system was devised some years ago that mathematically compares how a light source shifts the location of eight specified pastel colors on a version of the C.I.E. color space as compared to the same colors lighted by a reference source of the same Color Temperature. If there is no change in appearance, the source in question is given a CRI of 100 by definition. From 2000K to 5000K, the reference source is the Black Body Radiator and above 5000K, it is an agreed upon form of daylight.
An incandescent lamp, virtually by definition, has a Color Rendering Index (CRI) close to 100. This does not mean that an incandescent lamp is a perfect color rendering light source. It is not. It is very weak in blue, as anyone who has tried to sort out navy blues, royal blues and black under low levels of incandescent lighting. On the other hand, outdoor north sky daylight at 7500K is weak in red, so it isn't a "perfect" color rendering source either. Yet, it also has a CRI of 100 by definition.
CRI is useful in specifying color if it is used within its limitations. Originally, CRI was developed to compare continuous spectrum sources whose CRI's were above 90 because below 90 it is possible to have two sources with the same CRI, but which render color very differently. At the same time, the colors lighted by sources whose CRI's differ by 5 points or more may look the same. Colors viewed under sources with line spectra such as mercury, GE Multi-Vapor® metal halide or Lucalox® high pressure sodium lamps, may actually look better than their CRI would indicate. However, some exotic fluorescent lamp colors may have very high CRI's, while substantially distorting some particular object color.
Technically, CRI's can only be compared for sources that have the same Color Temperatures. However, as a general rule "The Higher The Better"; light sources with high (80-100) CRI's tend to make people and things look better than light sources with lower CRI's.
Why use CRI if it has so many drawbacks? It's the only internationally agreed upon color rendering system provides some guidance. It will be used until the scientific community can develop a better system to describe what we really see. It is an indicator of the relative color rendering ability of a source and should only be used as such.