The classic masters such as Leonardo Da Vinci, Michaelangelo or Rembrandt all used composition as key point of making their paintings better, more attention grabbing and aesthetically pleasing. They would produce hundreds of drawings and sketches when studying an object or person or pose as a way of building the composition up and finding the one they really felt worked.
The most simple way of looking at composition is following the basic rule of thirds and how an image can be divided up to make a clearer and more focussed piece.
Take this painting by Henning Ludvigsen for example, it can be broken down very simply by placing a grid over the top and breaking it down geometrically on the page. I painted a simplistic grid over the image to show the compositional layout.
There is a nice balance and weight across her body on the page that fits into the "golden sections" of the compositional grid. Without getting too mathematical as I don't do numbers, it basically works on the fibonacci sequence that occurs in nature through the structure of shells to the structure of leaves and fruit and has been shown to be one of the most pleasing forms to the eye. What I mean by "golden sections" is the separate boxes in which the form is equally balanced in where her arms meet along the vertical and horizontal planes.
Composition really makes a difference in the way images and concepts are perceived. Even in a 3D environment when the camera angles for cinematics and general movement aren't pleasing or confusing for the player, it becomes frustrating and annoying and can ultimately ruin a possibly great game. Composition is there to make the money shot that really sells the painting or game imagery and make it awesome to look at and with a simple oversight can ruin what has the potential to be great.