Woot! I also love threads like these, gives me a chance to flex some brain muscles...

Note this is going to be
completely biological in nature - no magic or divine intervention or the like.
Since the closest real-life model we have to compare to Drow is humans, I'm going to start with a little background about them, then work into some theories.
Biochemically, skin pigment in humans is primarily determined by a chemical known as melanin (though hemoglobin actually contributes a bit as well). In different ethnicities, this pigment has varying concentrations. In Africans, there's a high amount of melanin, Caucasians have a small amount, and albinos have none. Skin in it's natural un-pigmented color is white. (Aside: the same is not true for eyes, whose natural color without pigmentation is blue.)
Genetically, skin color is much more complex than a simple yes/no Mendelian relationship. I won't go into the genetics of albinos (or having blue eyes, they're similar) unless someone requests it. Generally, it's thought that skin color is affected by multiple genes, and if someone is
really interested I can explain how this works as well. The number of dominant genes you have determines how dark you are.
So that's very interesting (to me at least), but why exactly did this range of skin colors develop? There are several theories. The one most people have heard of is because of ultraviolet radiation. UV radiation can cause sunburn and skin cancer, and overproduction of vitamin D. However, the evidence suggests the big reason was because of folic acid/folate, which is detroyed by UV radiation (photodestruction). Folate deficiency is very bad, disrupting reproductive systems.
But, there's a problem with that line of thinking. We originated near the equator, where UV rays are strongest. So really, the question is why did lighter skins develop? This ties back to vitamin D. Melanin causes UV rays to be blocked, but a certain amount of UV radiation is necessary to produce vitamin D, which is essential for bone development and maintenance. As humans moved north and south from the equator, we began suffering from vitamin D deficiency. Lighter skin allows more radiation through, and it became a balancing of vitamin D production versus folic acid destruction.
Another, less popular, theory is due to temperature. Light skin is actually more resistant to cold temperatures than darker skin, and gets frostbitten less easily. While there is evidence to support this as well, the vitamin D/folic acid balance accounts better for the range of skin colors we see today.
Wow. So what's all this have to do with the Drow?
Well, for one thing mechanisms dependant on the sun are pretty moot underground, so color
really doesn't matter. Why then would Drow skin turn darker?
One theory could be that something in the environment actually contributes to the Drow pigmentation and aggression. Perhaps it has to do with that damn chemoluminescent moss that's always around, or something in their diet. If you can remove a Drow from that, or destroy a source of that, perhaps the aggression can be removed. Note there is precedence for this - ever seen Children of the Corn? While overdramatized, there is a corn mold that causes effects similar to PCP - severe agressive tendancies.
Another theory is protection. Since there's all this moss around shedding light and shadows, darker skin would be more advantageous for sneaking around and staying hidden. Predators would be less likely to see you if they rely on visual senses. Very similar to the classic story of moths during Industrial Age England.
A third explanation is simply based on natural selection. Suppose Elves at one time were as diverse in coloration as humans. If the groups were seperated by skin color, in a thousand years you'll have predominantly dark-skinned Elves and predominantly light-skinned ones. Why would such an event occur? Use your imaginations.
Yet another explanation, again related to the moss, is that Drow are... photosynthetic in a way. Perhaps Drow physiology takes light shed from that moss to fuel their bodies, much like a plant's chlorophyll green coloring takes energy from the sun and converts it to something useful. Suppose the Drow produce another agressive neurochemical by this method. An incursion and occupation into the overworld eventually pacified the rogue Drow, who eventually lost the ability to process the moss-light altogether.
And a final, editted in explanation. Suppose rage in Elves causes a chemical like adrenaline to be produced. Instead of being broken down like a human does, suppose this isn't broken down, or is broken down incompletely. This chemical is stored in the blood stream and nearby cells, resulting in a dark pigmentation to the skin, and also increases the aggressiveness and physical strength of the Elves as they lose control more and more.