To be able to properly colour correct and edit an image it should be done on a professional grade calibrated monitor in light controlled editing suite.
But that's just the basics and just this alone isn't enough as you also need to be able to "see" colour correctly to know what is right which is an art in itself. Back when I was 16 I worked for 7 years in Leicester's top pro photo labs where I was to learn the skill of colour grading in real darkrooms using enlargers and photographic paper. Read more here
Some consider editing to be just picking the best images, others take it a little further and may adjust some brightness. I like to go a little further still on some images.
A photographer doesn't actually have to have any editing skills as they can pay for a 3rd party to do all the colour correcting for them, but I prefer to keep 100% control of my images, as when I press the button that is only half the story.
The camera can only deal in 0s and 1s and so its in the editing that I can then start to put back some of that feeling that the camera couldn't see and create the image in more of a way that it was seen by the eye I can do this because I was there whereas a 3rd party editor does not have this benefit.
Its too easy to over create images in the editing, sometimes even though a single image may take me half an hour to edit I still prefer to keep it looking natural so you may not even know anything has been done at all unless you were to see the original version.
Here bride and Dad have just arrived at the Church but the cones outside the church did not leave enough room for the car and so the only place to park was here.
Video guys have to do their job too and can sometimes get into my shots