CIE Lab is hard to wrap the wits around, because it defines a color space that includes such things as, for example, a theoretical fully-saturated yellow at 0 luminosity, which is perceptually indistinguishable from black, all the way to (e.g.) bright blue at 100% luminosity, which is indistinguishable from white. From that, once you get the (esoteric, to be sure) concept, it's easy to extrapolate that Lab permits entire ranges of color to be defined that can't exist in CIE XYZ, the original CIE RGB, or HSB/HSL/HSV, which are based on what the average human eye can actually distinguish. (CIE XYZ is simply a mathematical representation of the original research work on human RGB perception done in the late 1920s.)
The huge conceptual difference between CIE Lab and other color models is that Lab is, by design, entirely device-independent. It is a sort of meta-color-space that happily defines colors that cannot be seen. You could argue that since color is a visual perception, this is a contradiction in terms, but CIE Lab allows any perceivable or realizable color to be very precisely defined, regardless of how it is created.
The RGB and CMYK models and their related color spaces are not device-independent. You can't define on-screen color as CMYK, because monitor colors are additive. Stage or movie lighting is RGB for the same reason. RGB doesn't work for inks or paint, since these are subtractive.
All this makes Lab sound like a theoretician's delight and a designer's nightmare, but there are many cases (especially in Photoshop) in which the Lab color model allows operations that are impossible in RGB or CMYK, because Lab completely separates luminance from color, unlike the other models available in Photoshop. There is no way in RGB or CMYK to change, saturate or desaturate a color without simultaneously altering luminosity, and vice versa.
Pantone Solids are defined as Lab values in addition to their ink formulations, so that there is no ambiguity as to the intended perceptual effect of that formulation under standard lighting.
The best practical text on the subject for designers and photographers that I know of is Dan Margulis' "Photoshop LAB Color." The subtitle, "The Canyon Conundrum and Other Adventures in the Most Powerful Colorspace" gives a hint of the content. It's an important and unique book that's had a permanent place on my bookshelf since it was published. I highly recommend it for anyone who wants to get a practical, as opposed to theoretical, grasp on Lab.
If you want to dig into this further, Sareesh Sadhakaran has some excellent and lucid articles for the Wolfcrow.com blog, such as this one.
