We all know how well glute bridges do your backside justice.
While having a nice butt may be aesthetically appealing, strong glutes are important for maintaining optimal hip and back health. For clients that naturally fall into lumbar extension (arch their lower back), the glute bridge with kettlebell pullover allows them to feel true hip extension without compensating through the lower back. Bringing the arms up overhead puts individuals in a position where it's easy to arch the lower back, forcing the anterior core to resist this default pattern.
When done properly, you should really feel your glutes, abdominals, and obliques firing hard to stabilize your entire torso. If you feel tension in your lower back, you're arching excessively and executing the exercise incorrectly.