Why do black people have light colored skin on the palms of their hands and on the soles of their feet?

This is true of all people--not just black people. It is because those are areas of the body that are least exposed to UV light.

http://wiki.answers.com/Q/Why_do_black_people_have_white_hands_and_feet

Thank you for your answer ferfer72 but I'm not so sure your link has got it right. Our under arms, for example, have far less exposure to UV light than the palms of our hands. Also most people wear shoes these days, thus the soles of our feet will have the same amount of exposure than the top of our feet.

Doesn't the color under finger and toe nails also exhibit lighter color and they (at least fingernails) are exposed as much to UV as the back of the hand. I believe the reason is that there is just genetically less melatonin in those areas of skin cells. Associated with melanin production in skin cells, perhaps the lack of hair follicles in the skin areas asked about has an impact on ultimate color.

https://en.wikipedia.org/wiki/Melatonin