Often the phrase "maintain a calm upper body" is thrown about by coaches and instructors and certainly visible in all expert skiing:
As you can see, the upper body remains relatively calm and still, relative to the movements of the lower body.
The basic idea is to not get the big mass of the body moving much in relation to the desired line, because that would create inertia that negatively impacts our skiing.
In fact, the upper body is not really still. To maintain this appearance of no movement, in fact there is significant effort in the core muscle groups, to separate the upper body from the lower body's movements and counterbalance and counteract the lower body (coiling).
However, this still generates two points of view, one that the lower body moves independently and that the upper body moves in reaction or to complement the lower body and achieve this look of stability. Another widely held point of view is that the upper body is stable and the focus is on moving just the lower body underneath.
There is truth to both of these. The upper body does tend to follow the lower body and if you only watch beginners and intermediate skiers inclining into the turns, you will see plenty of evidence. At the same time, at the high end, the upper body has a lot of inertia and momentum compared to the turn shapes and lower body movements.
The issue is more one of decoupling or relaxation: the pelvis and mid-body connect the two parts and relaxation would allow the upper body to continue on its path while the lower body moves independently underneath. While the beginners are usually locked up and stiff and do not decouple the two enough.
Some separation drills:
Tech talks / on snow: