Colour correcting is one of the most important things in video production. Much like good audio mixing and sound design, this type of work often goes unnoticed unless it's just not done or is done poorly. But even in those scenarios it's likely you won't know specifically why something doesn't look good, you'll just have this gut feeling that something isn't right.
There are a couple reasons colour correction is a must.
First and foremost, different light sources have different colour temperatures that affect the way colours look in camera. So during post production, colour correction is done to make sure that colours look consistent from shot to shot. The need for this can be minimized by adjusting the white balance in camera before shooting. White balancing is the process of adjusting the colour temperature in camera based on white colours in frame. If the white balance is too warm, the white colours will have and orange tint to them. Too cool and they'll have a blue tint.
Secondly, many advanced/pro shooters will shoot with a flat colour profile in order to capture as much colour detail as they can so they have more control over the way things look in post production. But if I shoot with a flat colour profile without correcting it in post, the result will be a very flat/muted/dull image. And nobody wants that.
I take pride in my work and want my clients to have the best product I can deliver them and so I take the time to pay close attention to every step of the production process, including colour correction, to make sure the colours are not only consistent from shot-to-shot but that they also fit with the client's branding tones/colours.