Here's a painting I did a few years back called Porziella:
the original painting
Here's the same image in grayscale - all color (hue and saturation) information has been stripped out:
And here's a color only version of it - all value differentiation has been removed:
Without value you can barely make out the various elements. It's hard to see any picture in there. Value is a far more powerful force than color in how we perceive images, and the world around us.
Value is so overwhelmingly important that one can almost say colors don't really matter, that is, in terms of whether the picture works or not. If the values in an images are working well, almost any color scheme will work. Here's the same painting with a new color scheme:
And here's the color layer by itself
I painted this in about 30 seconds, without thinking much about what I was doing. The color layout doesn't really adhere to the lines and forms in the underlying image at all. Nor is there any logic in terms of the color of the light source, the shadows, and so on. There are some vaguely warm splotches over the girl's face and hands, a cool color splashed across the sky area (and also covering much of the trees in the process), etc.
This haphazard approach unintentionally produces some beneficial results - different elements are naturally unified when given a single swath of color, similar to when light bounces back and forth between objects in proximity, or when they're bathed in an ambient light.
You can experiment like this using paintings or even photographs. Photographs are not a good way to learn about controlling value in painting, but for this exercise they're ok. MAKE SURE TO WORK IN LAB MODE when desaturating a source image, and when colorizing. RGB and CMYK modes do not accurately translate color to value, and do not accurately preserve values when colorizing.
Ultimately you want to be able to say something with color, whether you're creating a convincing depiction of a realistic scene, or using color more abstractly and expressively, or some combination of the two. In the beginning... and often for quite some time, though, getting colors simply to work, that is, to not look bad, can be a challenge for many artists. With opaque paint one must control value and color simultaneously. It is therefore critical to learn to see the two separately.
This little study should show you that color in painting is malleable, and even in representational painting is less bound to 3-dimensional reality than you may have thought. Value relationships are more critical - if you are having a color problem with a painting, chances are you are really having a value problem.