Thanks for the complement ref the images.
Color management is a common expression (you can Google it) - and in a nutshell means the technology and systems used such that all devices or media display the colors they can in a consistent way. The reality is that each device actually has its own responses and breadth of colors it can produce. For example one monitor's "purple" may not be the same as another's "purple", or indeed as per a defined reference "purple". A particular monitor may not be able to show as rich a red as another. Same between a monitor and a printer loaded with a certain type of paper and ink. In all examples, there will be a variance in color unless it is known and then compensated away somehow.
Color-management (which in its essence is a software RGB value-translation process) is what does that compensation by balancing the actual RGB levels sent to each device to ensure that there is that visual consistency in what is produced. To do this each device must be calibrated and characterised such that it has a known response
profile that can be used to translate the RGB values it needs or produces. The document itself (photo in our case) then must also be defined in terms of what the contained RGB values represent, hence a reference document color-space (like the common sRGB, aRGB, ProPhotoRGB) is also needed.
The actual underlying science and technology is somewhat more detailed and complex, but this is the essence of it.
Perhaps start here:
http://www.cambridgeincolour.com/tutorials/color-management1.htm
and there are then multiple articles out there (just picking some, including for C1):
https://www.xrite.com/documents/literature/en/L11-176_Guide_to_CM_en.pdf
http://help.phaseone.com/en/CO8/Output/File-formats/Colors-in-Capture-One.aspx
http://www.dpreview.com/articles/7270088913/color-management-a-walkthrough
Andrew Rodney aka
Digital Dog, an expert on the topic, often frequents this forum, and he provides links to his
own articles and videos (but if he's around I'll leave him as to which!).