Color management is an integral part of any color work. It allows you to achieve good consistent, reproducible color.
COLOR MANAGEMENT - You should care because without color management you cannot get consistent, reproducible color. Which means each time you print your file or image you may or may not get a print that looks the same as the last one.
Here at Graphics 360 we encourage our clients to design in Pantone oppose to CMYK or RGB when it comes to vector solid colors. This way, we can pull out our Pantone book and compare apples to apples. Since your monitor will look different than ours, this is the best way to match and compare. We take color management extremely serious. When most printers only calibrate a couple of times a week or even once a day, we calibrate before each job to ensure the most consistent color.