The pigmentation of your hair and skin clearly react differently when exposed to a lot of sunlight, as you've noticed skin turns darker, or tans, while hair can be lightened. I'll talk about the reaction with hair first, and then skin.

When you expose your hair to a lot of sunlight, you're basically naturally bleaching your hair. This is actually a similar process to when you go to the stylist and get your hair bleached, or exposure to chlorine in a swimming pool. Basically, exposure to sunlight causes pigment molecules in your hair to become rearranged, which changes how light is absorbed and reflected, and this rearrangement makes it look lighter in color. For a more complete answer, you'd need to go into some detailed chemical reactions.

The pigmentation of your skin cells is due to these cells releasing a protein called melanin. (The specific skin cells that do this are aptly called melanocytes.) The sun releases ultraviolet (UV) radiation on earth and exposure to UV radiation stimulates your skin cells to make more melanin. More melanin makes your skin look darker. UV radiation also can cause damage to the DNA in your cells which can lead to skin cancer. However, melanin can absorb UV radiation and protect your cells from (some) of its potential damage -- your body is actually quite smart in this way. Consequently, when you get a real tan, its your body's way of protecting you from future DNA damage since it knows from experience that you expose yourself to a great deal of UV radiation. Especially when at the beach or working outdoors, it's important to keep in mind that much exposure to sunlight can cause serious medical conditions later in life, such as the life-threatening skin cancer melanoma (along with other less harmful skin cancers).