Photo color management is the process by which proper application of RGB (red, green, blue) to create the colors of a digital image. And since color rendering differ in both the monitor and printer, the more reason color management should be applied.
Since digital photography is computer based, the accurate application of RGB must be accompanied by a color profile. In the absence of a color profile the computer will not be able to decode the profile information and define the exact color dissemination. It (program) will just have to guess what the color number means. Considering the huge numbers of color profiles, it is more likely that the program will miss to interpret the information.
To help the computer, there has got to be color information or “chain of custody”, like what color space was used, or how to use the color profile and assign colors for each pixel and others. Remember that when an image is sent to the computer and monitor, it will depend on specific color profile to atone for the discrepancies for the color footprint of the device. For example, too much blues on shadows, allows color profile to adjust and reduce the blues on the shadows.
Typically, color images are sent to the computer in jpeg format as files coming from digital cameras or any other device. As the digital information enters the scanner, the device has the option to attach a profile. And to to be certain that the image has been attached is to open in the App (photoshop for instance) and view the information at the bottom left of the program window. If the information does not appear on the view window, the image has been untagged.
Take note that the purpose of photo color management is to duplicate the image appearing on the monitor to that of the printed page. And most desktop printers are designed with custom profiles that may come out accurate. But, this is just a possibility and if the most accurate printouts are needed, then a custom profile must be made intended only for the particular printer that will deliver the printouts.
Remember, the end all in photo color management is how accurate the images taken by the digital camera must appear as live as possible on the printouts. Anything less defeats the purpose of the color management efforts.