For many home digital video filmmakers color correction refers to something that happens during post-production with non-linear video editing software. You take a specified video clip in your video editing software and you adjust different aspects of the color until it looks a little more appropriate to the color scheme that you have in your head or looks natural.
This is a great way to fix problems in contrast and lighting, especially if you just want to fine tune the over all color dynamic in the clip. At the same time you want to try to get the best color possible when you are actually in the field filming. Usually you will be fine with a quality digital video or film camera, white balance, and a good eye. There are some times when you will still be hard pressed to get the exact color system that you want. In these moments you will want to use a color compensating filter.