A swivel is defined as: "A turn on the ball of the stationary foot". There are many types of movements that contain the swivel action: Toe-heel swivels, Boogie-walks, pivots, Cha Cha swivels, tuck-turns, tripple-step turns, Waltz walk-around turns, slip-pivots, chase-turns, Tango promenade-close, Tango fans, half-moons, open-side-locks, etc. Swivels are primarily a Latin dance type of action, however, as you see from the above list, they also exist in the smooth dances.
The swivel is executed on a slightly bent stationary leg. The slight bend leg relieves the pressure on the heel of the foot causing the rotating movement to occur on the ball of the foot. Do not place your weight on the ball of the stationary foot by lifting through the ankle.
It is very important that none of the rotating movement be absorbed through the muscle structure of the body. The goal is for the swiveling action to occur between the sole of the ball of your foot and the floor. This means that the whole body must be toned and move as a single unit transferring the swivel to the floor.
For example: If the lady is doing a tripple step turn powered by her partner, she must be toned from the hand above her head all the way through her body down through her legs to the floor. Even though the swivel is occurring on the floor, the power and rotation is still directed to the center of the ladies body (center of gravity). In the tripple-step turn, each step of the tripple step has a portion of the complete swivel (the three steps making up a 360 degree turn). This means that each weight change must continue the swivel of the previous step. This only works if the lady is connected to the leader and using his power. If the lady tries to power it alone, the turn will be slow and hard to control. The feeling the lady has while turning, is not a feeling of a frozen body, but more of a feeling of using the leaders power and directing it to the floor. The lady is not a passive participant in the turn but an active part of the power process.
If you are doing solo turns such as chase-turns or open-side-locks etc., the same is still true. The swivel still happens on the floor, and the body must be toned to avoid any lost rotating power. The biggest difference is the source of the power. Since there is no partner connection for power you must supply it yourself. It comes from leg power to the floor redirected to a rotational movement through your center of gravity resulting in a swiveling action on the floor.
This sounds pretty complicated but in reality it is about a specific feeling. Once you have developed this feeling, it becomes an automatic response.