Obviously, exposure is a part of it: but it isn't the major part.
Most important, and this applies to all lighting, is the relative angle of the light to the subject, relative to the camera. In this case the light is only just out of shot, so te camera only sees small areas of the subject as being lit - the rest is in shadow. Try it with a round object and a torch in a dark room - move the torch around the object whilst you look from one particular angle, and you'll see how the shadows change and move.
The next element is the source of the light. A torch will give you a oint source, and this very hard-edged shadows. Put a piece of paper over the torch, and the source of the light effectively becomes larger, and so the edges of the shadows become softer - light comes from the whole area of the paper, and certain areas of the round object will 'see' some of that area and not others, and so will still be lit, but just not with as much light. That's why soft-lights work - they make the light-source a large area, and thus make the shadows develop gradually.
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