Center Point of Balance

Together with the center of gravity (COG), center point of balance (CPB) helps the dancer to better understand and control their movements. The exact location of the COG is always well-defined, however it significantly depends on the shape the body assumes. In contrast, the CPB during normal dancing (heads up, feet down on the floor) is always at the same place of the dancer body, although defined in a loose way: it is said that the CPB is in the general area of the solar plexus for the gentlemen, and navel for the women. The reason to distinguish this point lies in the following simple observation. If you put your feet together, you may move your head or your hips pretty far away from your area of support without losing your balance. But if you move your CPB just 2-3 inches away from the equilibrium position, you will feel a strong urge to step in this direction. Therefore awareness of your CPB, both consciously and instinctively, gives you a better control of the overall dance movement.

Spotting

This is a technique used by dancers during the execution of various dance turns. The goal of spotting is to attain a constant orientation of the dancer's head and eyes, to the extent possible, in order to enhance the dancer's control and prevent dizziness.
As a dancer turns, spotting is performed by rotating the body and head at different rates. While the body rotates smoothly at a relatively constant speed, the head periodically rotates much faster and then stops, so as to fix the dancer's gaze on a single location (the spotting point, or simply the spot). Dancers will sometimes focus on an actual visual spot if one is available (e.g., a light or other object), but if no suitable object is available they will attempt to end each head rotation in a consistent orientation. The spotting point may be another dancer, in which case the spot may move.

Pirouette

A turn on one leg, often starting with one or both legs in plié and rising onto Relevé (usually for men) or pointe (usually for women). The non-supporting leg is held in Passé. A pirouette may return to the starting position or finish in arabesque or attitude positions, or proceed otherwise. It is most often en dehors turning outwards toward the back leg, but can also be en dedans turning inwards toward the front leg. Although ballet pirouettes are performed with the hips and legs rotated outward ("turned out"), it is common to see them performed with an inward rotation ("parallel") in other genres of dance, such as jazz and modern. Spotting technique is usually employed to help maintain balance. Pirouettes can be executed with a single or multiple rotations.

Fouetté

A turn made by using a fouetté. For each turn the dancer stands momentarily on flat foot and in plié, as the working leg is extended in fourth position en l'air (or à la hauteur) front then whipped around to the side as the working foot is pulled in to touch behind the supporting knee. That creates the impetus to spin one turn as the dancer executes a relevé, rising onto pointe. Done properly, the dancer remains in place. The well known 32 consecutive fouettés (32 fouettés en tournant) in the coda of the "Black Swan" Pas de Deux from Swan Lake are a bravura performance designed to express the strength and triumph of the character.

(Above terms are from various articles on Wikipedia.)