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.
Using or Avoiding Color Compensation Filters
Color compensation filters are usually less useful than other filters as there are things that change the base image. Instead of using a color compensation filter you would be better off just adding the video filter in your non-linear video editing software. If you are going to use a color compensation filter right on the camera then you have to have a reason to do so.
One of the best reasons over all is to alter the color just slightly in order to counter balance against an awkward light source. This could be florescent lights, the sky giving too cool of a color, or possible a series of computer monitors shedding a blue light. Here you can make the color of the image more appealing, or even change the information of the scene by turning morning sky into a warm afternoon.
Common Color Compensation Filters
The most common color compensation filter is desaturation, or black and white. You can set most cameras to black and white right on there, yet it is usually better to just do this in post-production. The benefit of actually shooting in black and white is so that you can see the image in black and white so you can apply correct color contrasting. Sepia tone is also a common one to give a brown look that inspires and old film feeling. Other color compensation filters are very specific to lighting sequences so try to find ones that are going to be calibrated directly to your circumstances.