Gravity: Everything pulls on everything else. On Earth, we are constantly being pulled toward the center of the Earth by a force called gravity. Gravity is the reason why everything that goes up comes back down.
Center of Gravity: The average position of weight distribution. When a dancer jumps the center of gravity is in his/her torso.
This applies to ballet as well as on everything else in the world. It applies to turns that have a center of gravity, simple steps, but most importantly to jumps. In ballet when a dancer jumps he/she is jumping against the force of gravity. The dancer exerts a force on the floor, which according to Newton's third law, pushes back, giving the dancer the impulse, he/she needs to jump.
When the dancer is already in the air gravity is what pulls the dancer back to the floor, but gravity only affects the vertical motion of the dancer, not the horizontal motion, which is what allows the dancer to extend his/her legs in different jumps. As the dancer is in projectile motion during the jump, the center of gravity of the dancer follows a parabolic path, with the vertex being the highest point of the jump. However, his/her horizontal motion is not affected. (Figure 5)
Figure 5