Rn, here is an explanation from the website MasterClass:

5 Benefits of Doing Turkish Get-ups
Consider the many benefits of regularly performing Turkish get-ups.

Full-body workout: Turkish get-ups work major muscle groups across your entire body, including your glutes, traps, lower-back muscles, hamstrings, triceps, lats, and calves.
Core strength: You rotate through several positions during Turkish get-ups, engaging your core throughout the entire exercise. By extending the kettlebell above your head during the workout, you put special emphasis on your oblique muscles.
Improved posture: Turkish get-ups activate muscles in your upper body that help improve your posture.
Shoulder stability: By holding a free weight directly above your shoulder during Turkish get-ups, you enhance shoulder mobility and stabilization. Turkish get-ups also strengthen the muscles around your shoulder joint.
Lower-body mobility: Turkish get-ups require hip flexion as you transition between different positions. By engaging your hip flexor muscles, Turkish get-ups are useful warm-ups for other compound exercises that use a hip-hinging movement, like the deadlift.