Color (or colour) correction is a broad topic. But generally is it trying to get the most accurate colors out of an image.

The basic problem at hand is that your eye automatically color corrects everything you see. A piece of paper looks just as white inside under a lamp as it does outside in the sun. However the two lighting conditions are really very different. When a camera captures images of that same sheet of paper under the same circumstances, you will see that the inside light is most likely orange, and the outside is white or blue.

Your camera will generally do an okay job correcting for this fact, by applying a white balance (the specific color white should be under any given type of light). But sometimes it is wrong or slightly off. Additionally, A photographer may choose to tweak the color of lighting for artistic reasons, or because of a mixed lighting that doesn't match.

There are a variety of ways to accomplish this in photoshop, lightroom, and even in your camera. If you have the option, shoot in RAW for the most flexibility.