Back extension rolls are a fundamental skill in women's artistic gymnastics and should be taught properly in the first three to six months of coaching.
What makes the back extension roll so important? The answer lies in the technique of a properly executed back extension roll which carries over to other core skills.
The most important of these core skills are free-hip circles and backwards giant swings on uneven bars, but the muscle memory in back extension rolls also carries over to related skills.
Put simply these skills all share the need for the upward lift of straight, tight arms that comes from shoulder extension and the hollow torso position as you can see in this comparison picture:
The video below from TeamCentralGym shows some very good basic drills for shaping back extension rolls in young gymnasts:
The back extension roll also applies to more advanced gymnasts. Mas Watanabe shows how he incorporates this skill into drills for a blind change:
Along with using this skill in progressions and specific technical preparation, coaches can (and should!) make shoulder extension a part of strength conditioning.