Use this tool to raise the shadows or darken the highlights of an image.
In order to separate the dark areas from the light ones, a lightness mask (invisible to the user) is created. There are two algorithms for doing this; one blurs the image, while the other retains sharp edges between light and dark zones. Neither one is "better", both have their own merits. The soft mask approach can lead to halos, but it is quick. The sharp mask is slow, but it doesn't cause halos, though it can cause edge artifacts at close inspection.
Allows you to brighten the darkest parts of the image
Allows you to darken the brightest parts of the image.
Shadows/Highlights Tonal Width allows you to control how bright an area must be for it to be affected by the highlights slider, and how dark an area must be for it to be affected by the shadows slider. Though the underlying math is a bit more complicated, think of a histogram - the highlights tonal width specifies the range of tones from the white end of the histogram which the highlights slider will affect, and the shadows tonal width specifies the range of tones from the black end of the histogram which the shadows slider will affect. The higher the tonal width value, the more tones are affected.
The value of the Radius slider influences the effective area of the Shadows and Highlights sliders.