Think of the bottom sliders as input values and the top sliders as output values. When the top left (black point; output) is set to zero and your bottom left slider (black point; input) is set to 5, then all pixels with a value of 5 or less are mapped to zero. Conversely, if you set the input point to zero and the output point to 5, then all pixels with a value of 0 will be mapped to 5 (making the blacks "less" black).
Typically, the input sliders are set to values where you want pure black & white to be, and the top sliders are set to 0 & 255. This produces a full-range image. In some cases where you'd want a less contrasty look to an image, you'll set the output values to 20 & 235 for a soft, low contrast image.
Thanks Chris - well put and crystal clear.