Ballet and certain types of dancing is all about body movement, so its important that the lighting emphasizes this. This is where side lighting comes in. To be clear, in this case the side lighting literally comes from side, not from ceiling height at sides of stage, but rather literally on the side with fixtures placed horizontally to the stage from ground level to height of Performer. Commonly referred to as Shin Lights and Headlights. (This was the design concept of the CHAKRA)
Lighting from the side like this captures and highlights the mystique of body movements. Less emphasis is placed on the front and rear of performer When Properly done side lighting can enhance body movements and give the perception of "Floating". Reducing the Front and rear lighting leaves less light on the stage which further enhances the effect.
Next time you enjoy such a performance, remember the creative and highly scientific nature of the lighting design that is present.