In summary, the sun lightens our hair because it bleaches it, but it darkens our skin because our cells respond to sunlight by producing pigment to block future exposure to the sunlight. Just like bleach can whiten our clothes, sunlight can destroy the pigment in our hair, making it a lighter color -- for a more detailed chemistry answer, check out this link:

The reason our skin darkens has more steps involved. When our skin is exposed to sunlight, which contains dangerous UV light that can cause damage to our DNA, our skin responds by trying to protect us from the harmful UV rays in the future -- it produces pigment called melanin. Melanin is what is responsible for skin color/tones (more melanin means a person has darker skin). Melanin absorbs the harmful UV rays so they do less damage to our DNA. However, even though our skin works to protect us all the time, it can only do so much -- repeated tanning and sunburns can cause melanoma, a potentially fatal skin cancer (due to mutations in our DNA). For more on sun tanning, see this link:

So, be sure to always wear that sunblock, and stay away from those tanning salons! And be especially wary of "spray on" tans -- these "tans" are often pigment from vegetables that may make your skin look darker, but, because they don't make your skin make more melanin, you're just as susceptible to getting a sunburn as if you weren't tan at all.

Skin is alive; hair isn't. Both contain melanin, the pigment that makes hair or skin dark, which is destroyed by ultraviolet light (this is why it can absorb UV), but when melanin in the skin is destroyed, the skin reacts by making more melanin, more than it had to begin with. Hair, being dead, can't react that way, and so over time will get bleached.