I am familiar with process management, and the work it entails-it's part of the curriculum I teach. Color management is just another process.
Cool! Fwiw "Color Management," of the ICC style, is a bit of an indirect sort of thing. It's fundamentally based on measures of human perception, and various machines - digital cameras, etc. - do not necessarily match same. It's kinda overly complicated to explain here.
Let me give a very brief (for me) explanation... in the late 1920s (I think) there were some "color-matching experiments" documented (look up Wright and Guild? ... going from memory). Essentially, they used three colored lights, adjustable in strength, and had various people to try to match a bunch of spectral colors by dialing up the strengths of their 3 colored lights. More complicated than what I'm saying. The results were summarized into a set of "color matching functions," where each spectral color (defined by wavelength of its light) has three values, one for each of the colored lights. Some of the values had to be negative, roughly meaning that the color could NOT be matched, except by putting an opposing color on top of the spectral color. Now, it turns out to be mathematically possible to recalculate the color matching functions for different colored lights, and even for hypothetical, but impossible, colored lights. So, apparently in order to eliminate negative values in the color-matching functions, they invented some "impossible" colored lights, so-called "imaginary primaries." So today's commonly used color-matching functions are based on same.
With that background, let's say that you want to determine the "color" of some given test patch, whether it's Macbeth ColorChecker or your own paint chip. What you would ideally do is to first measure the spectral reflectance of the test patch through a range of roughly 400 to 700 nanometers, the main sensitivity range of the human eye. (This is done using a spectrophotometer.) You also need to know the spectral makeup of the light source used for viewing the test patch. Finally, for each wavelength you would multiply the light source times the spectral reflectance, and then times the CIE color-matching function. This gives a set of CIE coordinates which, after normalizing vs a perfect white reflector, can then be converted into something like CIELAB values (L*, a*, and b*). CIELAB uses, as I recall, a so-called D50 illuminant, a hypothetical source roughly equivalent to daylight with a color temperature of 5000K. And yeah, I know how to (or at least used to) do the calculations.
Now, I note that your sample image of a Macbeth ColorChecker has a set of three numbers, presumably some version of RGB in 8-bit, 0 to 255, numbers. Now, those numbers are actually meaningless without specifying a so-called "color space" for the RGB system (typically this space might be what they call sRGB, where the primaries are defined, as well as an illuminant (I think D65 for sRGB) and a tonal response from nominal black to "white").
Having put up my set of smoke and mirrors, I would now ask, do you think you know what the values of the Macbeth ColorChecker are? So this is the sort of thing you'd be dealing with when using a ColorChecker to assist in getting the colors "right." It's a fairly big learning curve.
I'll make another post regarding the actual (original) Macbeth ColorChecker.
Also, glad to answer, or at least try, any questions, within reason.