Turning a hand's-width of motion into a millimeter of motion
Motion scaling is the deliberate reduction between how far the surgeon's hand moves at the console and how far the instrument tip moves inside the patient. A typical ratio might turn several centimeters of hand travel into a few millimeters of tip travel. This matters because human fine motor control is much better at making a large, comfortable arm movement precisely than at making an equally precise movement over a tiny range, our hands are simply not built to reliably place something within a fraction of a millimeter using only fingertip motion. By letting the surgeon move naturally over a comfortable range and having the robot compress that motion down, the system converts the surgeon's existing dexterity into surgical precision it wouldn't otherwise have.
The scaling factor isn't fixed. Surgeons can typically adjust it depending on the task, a coarser ratio for repositioning an instrument across the surgical field, a finer ratio for delicate work like suturing a small vessel. This is conceptually similar to adjusting mouse sensitivity for different tasks, except the consequences of a mismatch are far higher. Too coarse a ratio during fine work risks overshooting delicate tissue, too fine a ratio during repositioning makes the surgeon's hands travel awkwardly far for ordinary movements. Getting this tunable relationship right, and making the transition between settings intuitive rather than disorienting, is itself a significant part of surgical robot design.