Since films start to use color in 1939 color become a very important part of story telling. This because colors have means and help to tell the story.
If Sin City would have been shoot in color, instead of B&W plus one representative color per sin, it would have been a very different movie.
Color is very important in telling a story. They help to in establish: mood, the tone of the movie. If you are shooting a funeral scene, usually, you are using dark and unsaturated color. If you are shooting a fairy tale story you are using saturated and bright color, for example.
I find interesting to analyze the color palette use in movies. Some of them have a very specific color palette as 12 Years a Slave has a green-brown one and have very little red in it.
Some movies have different color palette for different part of the story as in Moon Light.
One of my favorite website to find out color palette of different movies is http://moviesincolor.com. In it you can find a vast gallery of still from film with underneath the color palettes divided in light, dark, medium and general. plus several link to interesting articles about color in film.
Here some other interesting link about color:
https://www.youtube.com/watch?v=aXgFcNUWqX0 this channel is very interesting for many aspect of story telling.