They train the forearms, a bit of biceps, latissimus dorsi and a bit of core strength and leg strength, mainly though for stability.
In the video you will notice how far back Lauren's elbow goes, this is to involve the hips more and shoulders less, which will help develop the lats more. Notice also how her back leg is outstretched her and her front leg is bent.
The back leg is stretched back to allow for a stable base as well as a stretch in the muscles of the back as the arm extends down and forward.
The front leg is bent and the foot is pushed in to the ground to help keep the upper body stable.
She also has her hand resting firmly on the bench to give stability and more power to get the dumbbell up.
One instruction I gave her was to rotate her right hip down as she pulled her elbow up, this is to help her engage her back muscles more.