Lighting ratio is simply a way to communicate the difference in level between the key and the fill as it falls on the subject. A ratio of 2:1 (something like the image on the left) would be much more evenly lit than a ratio of 5:1 (something like the image on the right). My numbers for these particular shots are guesses, by the way, since I did not measure the light on location--but you get the point.
In this film, which is a children's film, the decision was made in pre-production to keep it bright and happy. The best way to accomplish this goal was first of all to choose colorful locations, costumes and set decorations. Equally important, however, was to keep the lighting ratio low. This is why the image on the left is the only choice that could work for our film. The image on the right is much more moody, gritty and dark, which may be perfect for another film. And, in fact, it could work in our film, but only if we were trying to accomplish a dark, scary effect on one of the subjects.
Why is it important to know all of this? Well, it is the language of lighting. How else could we describe to the second unit director of photography how to light scenes that will match the first unit? How else could the History Channel hire DP's in ten locations to shoot interviews for a show and have them all look like they were shot by the same crew? It is critical to be able to describe to someone else what you are looking for, and that is where knowing your lighting ratio is important. It is important for your own shooting as well. If you can have a clear idea of the ratio you want while you are lighting each shot, you will end up with a much more consistent-looking project in the end.
