The noise is random, and clumps in patches like raindrops on a sidewalk. Sometimes those patches happen to overlay the corners of her mouth or her eyes, and alter her expression. This is analogous to small changes with da Vinci's brush. When the noise is displayed, you can drag the noise to try other positions.
The most prominent change is in the shape of her mouth: in the sad face the mouth is flat, and in the happy face it is curved upward at the corners. This is hardly surprising, but it is interesting that even random noise can affect our perception. Expressions are often the result of subtle changes in facial features, so humans indeed develop amazing sensitivity to these changes.
While it may be true that we are also sensitive to overall changes to facial structure (low resolution), the diagram above illustrates that changing small details can affect the mood we percieve. A few pixels of change switches her from happy to sad.