ICC printer profiles address several different needs.
Pleasing color prints, reproducible color prints, and accurate color prints.
"Pleasing" is what most people want out of their printer. They have an image on screen and want to print it and have it look good. Profiles provide a way to change colors and tone in such a way that the print is both pleasing and reflects what is displayed on screen. ICC profiles call this "Perceptual Intent."
Reproducibility is achieved by using the same profiling software for different paper and printers. Alternately, precision reproducibility of "pleasing prints" where one may use different printers, paper, and or profiles in the future can be achieved using ICC profiles operating in reverse. This is a way to record the colors actually printed when using profiles to create pleasing, but not color accurate, prints. This is typically done by converting the image into printer space using the print profile and selecting "Perceptual intent," followed by converting back to an RGB space using Relative Intent." In the future that image can be printed using Relative Intent and it will be almost identical to the original printed image. There is some loss of precision in the back and forth but it is typically not perceptible even looking at side by side prints.
"Accurate," in the scientific sense is, provided by profiles using either Relative or Absolute Colorimetric Intent. Accuracy is limited mostly by the printer's gamut but also by the smoothness of the printer color to changes in RGB values, the accuracy of the profile's lookup tables, color measurements from which the profile was generated, and drift in the printer over time, temperature, humidity, and operating environment. For instance a printer that has been idle for a few weeks might have significant colors shifts initially.
Relative Colorimetry scales Lab(100,0,0) to the media white points which is often slightly off white. This produces prints, with white borders, that appear the same due to human color adaption to the border "white."
Absolute Colorimetry prints, within the limits of the overall technology, the exact color specified. This is used for proofing and replicating industrial colors. If you are asked to print the color Lab(70,20,20) you would do so using Absolute Colorimetry. It's also very good for reproduction work where you want to exactly duplicate another print or document including keeping the same white point tint as the original documents.