The Swing Out is the fundamental Lindy Hop move. It is an essential building block on which to learn many other Lindy steps and moves.
The Swing Out begins with the lead bringing the follower towards him after his rock step. Then they triple-step around each other trading places. The lead should have his right hand around the follower's waist. Their bodies should always be opposite and parallel, facing each other.
If the rotation is done correctly, centripetal and centrifugal force will create a tension between the two dancers.
Now that the dancers have traded places and they've built up some momentum, the final part of the swing out happens. On the fifth count of the music, the lead will bring the follow around trading places again. The follow will swing out away from the lead and usually make him look good by gyrating or doing some fancy footwork.
Most leads and follows need lessons, practice, and a lot of patience to master the Lindy Hop swingout. To make things even more confusing there are two major styles of Lindy Hop, Hollywood Style and Savoy Style that each bring their own character into the swing out.
Savoy swing outs came first, since Savoy is the original Lindy Hop style. The steps are bouncy and the body posture is relaxed. The dancers can also freely move about the dance floor.
Hollywood swing outs came later, when Dean Collins brought the Lindy Hop to California. The west coast dancers developed their own unique style of Lindy Hop. They incorporated an upright body posture, added a distinct whip to the swing out, and made Lindy Hop into a smoother, less-bouncier, slotted dance.
There are numerous variations on the basic Lindy Hop swing out. If you'd like to learn the swing out, classes in Hollywood or Savoy style Lindy Hop are available in most cities.