A colour management system is a set of techniques and technologies used to ensure that colours are represented and reproduced consistently across different devices (like cameras, monitors, and printers) and in various media.
Colour management systems aim to control the way colours appear from the initial capture or creation, through display and editing, to final output, ensuring that what you see on your screen or print matches the original colour as closely as possible.
So colour management is about the accurate reproduction of colour.
An artist may want to accurately reproduce a colour they see in a natural scene using oil paints.
A designer may need to identify colours in an original photograph and then ensure they appear the same when printed.
An advertising company must ensure products look the same across all the platforms where consumers encounter them.
A filmmaker may want to use consistent colour grading across every scene within a movie.