Execution:

The athlete lies flat on their back and actively pushes their belly button down towards the floor, lower back touching the ground. Squeezing the abdominals and glutes, the athlete takes their arms above their head and keeps their legs straight and toes pointed.
The shoulders and legs are then taken off the ground, the athletes head should come off the ground with their shoulders, head in line with the shoulders. The athlete needs to remain tight and find the lowest point they can have their legs and shoulders without touching the floor or breaking the lower back (ie: where is starts to arch off the floor).
The arch (AKA superman) is the opposite of the hollow, the athlete lies face down with arms covering ears and feet squeezed together. The athlete simultaneously lifts head, chest and shoulders as they lift their heels up and squeeze their glutes.

Purpose:

The hollow and arch are key gymnastics movements, they are used for the pull up, ring dip, muscle up and handstands.

Programming:

Most often as a skill development piece in the warm ups, commonly used in a tabata style (20 sec on, 10 sec off).

Variations:

The hollow and arch can also be done from the hang, either from a bar or rings and is usually called a “kipping swing”.