(⇒ From old Shetland word related to 'troll'.)
The concept of "dark elves" is not a new one. Mythologies paint two kinds of pictures of elves or elf-like creatures - there are good and bad spirits of the forestlands. J.R.R. Tolkien fashioned his elves after the good spirits. But obviously, fantasy writers needed something like the Scandinavian svartalfar or the scary, destructive thing from Goethe's Erlkönig...
The drow are one example of such race, and quite probably the best known. The drow first appeared in E. Gary Gygax' Oerth (Greyhawk), and after that they (at least) appeared in Abeir-Toril (Forgotten Realms), the world of Ed Greenwood and contributors. The first module to feature drow was Vault of the Drow (AD&D module D3, TSR#9021, by Gary Gygax, first published by TSR inc. in 1978).
Of course, the drow as such are specific to Dungeons and Dragons and the derivative material of thereof, but other authors have used the same ideas - for example, the world of Midkemia has the Moredhel (and let's not link Terry Pratchett...)
(Note: Since I don't have any Greyhawk material at hand, the following describes mostly the Forgotten Realms drow. I doubt there's that much difference between the worlds, though...)
The drow are descendants of earlier elf subrace known as Illythiiri. Worshippers of evil goddess Lolth were cursed by the good elven goddesses and banished to the Underdark.
The drow are quite like most elves what comes to the body build and size - usually just a little bit smaller and skinnier on average. The facial features are quite similar. The most radical difference is the skin and hair - the skin tends to be of very dark color (obsidian black, dark gray, or in rare cases even dark blue), and hair is white (or sometimes pale yellow). The eyes are very pale, often lilac, silver, pink or blue. The drow can see very well in the dark, but do not particularly like to operate in bright light and bright lights can disorient them momentarily. Like other elves, they have very long lifespans.
The drow are usually known among the other races as vicious and evil. It would be easiest to describe the drow as elitists and racial supremacists, believing the world should belong to them alone. The cities of the Underdark operate efficiently, if not just plain cruelly, under the guidance of the matriarchy. The name of the game is easy: Be an useful part of the society or get ground to dust. You can trust nobody farther than you can throw them, and you can only influence others through power (be it psionic, physical or magical) and fear.
However, while they are undoubtedly an evil race, they're also able to do good - even when that is very rare indeed and is usually done to build very tangled conspiracies that eventually lead to (understatedly) bad things. Their powers of good, if any, are usually expressed in form of arts: the drow are, like the other elves, capable of crafting beautiful objects of art, and their subterranean architecture is, if possible, even more amazing than anything other elves or dwarves can produce. And while other evil races craft crude weapons to poke their enemies with, drow clothing, weaponry and armor are legendary and in quality second to none (though it must be noted that most of their weapons are and armor are bought from Duergar). Their magic makes these items go bad in sunlight, though...
Most of the drow live in the Underdark, the vast underground realm, in various city states. The vast majority of these city states, and thus vast majority of the drow, bow before Lolth, the spider goddess, Queen of the Demonweb Pits. Lolth's worshippers believe, basically, in the inferiority of everything else except the drow females - thus, the cities are matriarchal and ruled by priestesses of Lolth, with the males only on secondary positions, only a tiny little bit higher in the ranks than the slaves - men are more of breeding animals and warriors. There's no marriage or courtship as such, and love is virtually nonexistent. The status matters; drow with no home or work prefer to join the army, because otherwise they'd get kicked around and ultimately sacrificed to Lolth.
There are only few exceptions to this kind of society in the Underdark; one notable exception is Sshamath, a city ruled by male wizards. Some believe there may be other forms of drow governments as well.
Not all drow are matriarchal, and not all stay below ground. Another important god is Vhaeraun, favorer of thieves and acts of evil on surface world. Vhaerun's worshippers tend to have more equality between sexes, but Vhaeraun's and Lolth's ideas rarely mix. Vhaeraun has more worshippers among the surface world drow. The major drow settlements on surface world can be found in Cormanthor, former site of the Elf Council.
It is interesting to note that while the drow are known for their evil ways, one of the most famed individuals is Drizzt Do'Urden (a follower of forest goddess Mielikki) - a good-hearted drow ranger, fighting against his evil kin. And Drizzt isn't the only drow that has good heart. Foremost, this is evidenced by the third big deity in the drow pantheon: Eilistraee, the Dark Maiden, Lady of the Dance, daughter of Araushnee (who became Lolth), is a goddess who encourages goodness and kindness, and return of the Drow to the surface to live in peace with other races. There has been a lot of rebels and good-hearted drow, even when they are far less in number.
Ed Greenwood, Skip Williams, Sean K. Reynolds and Rob Heinsoo. Forgotten Realms Campaign Setting, 6/2001. Wizards of the Coast, Third edition, 6/2001. ISBN 0-7869-1836-5.
Open Gaming Foundation and Wizards of the Coast, inc. "Monsters (E)". System Reference Document, 25/11/2001. Online. Author information missing. <URL:http://www.opengamingfoundation.org/srd/srdmonsterse.html>. Accessed 2003-01-12.
Sean K Reynolds. "Drow Social Relationships". Wizards of the Coast website, 28/10/2002. Online. <URL:http://www.wizards.com/default.asp?x=books/fr/drowsocial>. Accessed 2003-01-12.
Thanks to Tiefling for a couple of corrections.