Torso rotation is the foundational way to train the obliques: you rotate the trunk against resistance while the hips stay relatively fixed, so the internal and external obliques have to produce and resist the twist. It's the generic rotational-core movement a drafted program references by default — the load can come from a machine, a plate, or just your bodyweight.
By default it means the Rotary Torso machine: you sit with your hips and thighs locked into the seat and rotate against a weight stack. Because the lower body is pinned, it's the cleanest, lowest-skill way to load the pattern — the safest place for beginners to feel the muscle and the easiest to overload, which is why the machine is the default when a plan just says "torso rotation." Without it, the same pattern loads well as the Russian twist (a plate or medicine ball while your own core stabilises) or the bicycle crunch (a bodyweight staple you can do anywhere). For a harder full-core version that stacks rotation on hip flexion and grip, see the hanging knee raise with twist.
For whom: beginners learning to isolate the obliques, anyone training around a cranky lower back who wants controlled rotation, rotational athletes (golf, throwing, racket sports) building trunk strength, and advanced lifters adding safe high-rep rotational volume at the end of a core session. Pick the load that matches your setup — the machine by default, the Russian twist or bicycle crunch when you're training without it.