The barbell jump squat is performed like a vertical jump but with a barbell on your back. It develops lower body strength, power, and force development and even increases muscle mass.
The barbell jump squat primarily works the muscles of the legs.
That is, the quadriceps, hamstrings, glutes, and calves. Your trunk and upper back muscles are also used to support the barbell when jumping.
However, these muscles are not the primary target or exercise.