Ballout: A ballout is a trampoline skill that starts from a 3/4 dive or from a back drop and rotates forward in a 1&1/4 front somersault breadth axis lands on two feet. A double ballout is a back drop with 2&1/4 front somersault to the feet. In trampoline, double and single ballouts are common.
In artistic gymnastics, the back drop, ballout is a great lead in practice skill and progression for handspring front vaults and toe on front bar dismounts. For this progression, gymnasts should land the back drop with their arms over head so they can used them to stretch up and over into the somersault rotation.
This video can give you, at least, a visual idea of what the skill is, even though it is lacking in height, amplitude and ideal execution: