Color management remaps RGB/CMYK numbers from one color space into another, from source to destination, so that the colors appear the same. That's basically it.
A simple example would be a file in the ProPhoto color space, displayed on a monitor. If you just throw the RGB numbers directly at the monitor, it would look horribly wrong. So what happens is that the numbers are recalculated to give the same color appearance in the monitor's native color space.
Color management always requires two profiles: one describing the source, and the other describing the destination. Then one is translated into the other.