This refers to settings on how to treat different settings in linked images. Illustrator doesn't remember what was chosen when each image was placed into the file. So you have to re-select it every time you open the file. You might not know what someone has chosen who handed a file to you. So Illustrator at least informs you that someone at least had a different default setting than you have, thereby assuming that people will always want to treat each and every image the way they set up their color management.
Yes, it is a vital setting, because it determines how colors will be converted when embedding the file, printing or savng a PDF.