Note: This is on Drow in general and does not take into account communities that follow different rules, e.g. S'shamath, which is ruled by mages and where females are merely the equals of males. Nor is Lolth's worship dominant in S'shamath.
The dark elves (also known as drow) are evil cousins of the other elves. Driven beneath the surface long ago by the light-loving elves, these sinister beings have made a home for themselves in what they call the Underdark, the niche they have brutally carved in the underground caverns. They have become the masters and mistresses of dark grottoes, and any intelligent creature shuns them. Originally the drow were simply elves who held more with the tenets of might than those of justice. In their quest for more power over life, they inevitably began dealing with the forces that would one day corrupt them. Their elven brethren, dismayed at the initial change in their formerly peaceful kinsmen, sought to reason with them. The drow, seeing this effort as aggression, responded by slaying emissaries and invading elven cities. Convinced of the evil of the drow, the other elves banded together to drive them from the land.
(Toril and Faerun specific: During the First Crown War, the Ilythiiri made several unsuccessful attempts to conquer Faerûn (actually they conquered Southern Faerûn and to the north up to Shantel Othreier, and perhaps only the intervention of Corellon Larethian had stopped them), and at the time of the Fourth Crown War, they turned to Lloth and the other outcast Seldarine in the Demonweb Pits who gave them powerful magic and fiendish allies, as a reward for allegiance. One of these was a balor named Wendonai. He bred with the Ilythiiri, giving them a taint.)
A long, painful war marched across the centuries; elf slew elf, and great magicks flew. Much of the world lay in devastation, soaked in the blood of elves.
(Toril and Faerun specific: Wendonai was a balor lord who, in -11500 DR was tasked by Lolth to seduce the Sethomiir clan, rulers of the Ilythiiri into her worship and grant them evil magics. He succeeded and was probably the greatest (but by no means the only) influence on the fall of the dark elves.
After many malicious acts and abuses of elven magic, Corellon Larethian banished the dhaerow (traitors) whom Lolth used to be responsible for (and most of whom still secretly worshiped her) to the Underdark. A horrid magical storm known as the Dark Disaster laid waste to Miyeritar. History (as written by the victors of the Third Crown War) says that Miyeritar's attempts to stop Aryvandaar's armies caused the Dark Disaster. In truth, the fell magic that produced it was called forth by Vyshaantar high mages and proceeded unopposed because a Vyshaantar assassination campaign had destroyed many of Miyeritar's high mages in the months before. The Dark Disaster hung over Miyeritar like a funeral shroud for months, and when it's cloying mists and bloody rains finally dissipated, the once-proud forest had been reduced to a blasted, poisonous wasteland. Although many of Miyeritar's original inhabitants had fled long before the killing storm hit, innumerable innocents died horribly.)
Finally, however, the good and neutral elves triumphed, and they drove the drow underground. The corruption of the drow echoed in their appearance, for their skin darkened and their hair turned white. Their eyes glowed red—further evidence of the fires burning within their breasts.
(Toril and Faerun specific: After the so-called “Descent” into the Underdark, the warlike drow immediately began violently trying to establish their own territories in the Underdark around -9600 DR. They stole dwarven magical items and used them against their former masters, creating the enmity that still exists to this day. They also seized the gold dwarf cavern of Bhaerynden, creating the kingdom of Telantiwar. The drow then began fighting amongst themselves, trying to establish a single ruler. The attempt failed, only resulting in a great magical explosion that destroyed this large cavern, forming the Great Rift.
The surviving nobles took what they could and left to establish their own realms elsewhere in the Underdark. This time was known as the Scattering and produced most of the cities in which the drow live to this day, including as Sshamath, founded beneath the Far Hills in -4973 DR, Menzoberranzan, founded in -3917 DR, and Ched Nasad, founded in -3843 DR. On the surface the drow are sometimes referred to by Elves as The Ones Who Went Below.
During this time Wendonai continued his work, acting as advisor, tutor and sometimes consort to the most powerful drow Matron Mothers. He tried to claim a little power for himself by leading a sucessful drow and duergar attack against the Elven Court in -4400 DR called the Dark Court Slaughter. Wendonai's efforts at personal growth over the next two millenia earned Lolth's ire as she had no intention to let the drow return to the surface. Lolth withdrew her favour of the demon in -2549 DR and the Matrons followed suit.
The taint of Wendonai allows him to hear the thoughts of the tainted. It is only the Ilythiiri who carry it, and it gives them their cruel and arrogant nature. The drow, as they were now named, have always believed that they were punished for being “successful” and have remembered this perceived slight and vowed eternal revenge, still claiming the surface world as rightfully theirs.)
The drow are reputedly as widespread as the other subraces of elves—perhaps even more so. No one not of drow heritage knows exactly how far their underground holdings extend. It is well known that they have a certain grasp on interdimensional magic, for they use it to travel long distances. They hate the light, and they have extensively researched ways to travel while avoiding the sun, which is anathema to them. The drow have extensive tunnel networks, which may or may not canvass their world.
Drow are typically shorter than other elves, and they retain the Dexterity common to elves. In all other respects, save their height and coloring, drow resemble their aboveground cousins.
Drow craftsmanship is truly a marvel to behold, wrought with strange and intricate designs. Unfortunately, their works are unable to exist outside the drow world, and the items disintegrate, albeit slowly, when away from the radiation of the Underdark.
Their society is usually matriarchal, with the female drow holding the majority of power. Male drow are entrusted with the relatively unimportant jobs of swordplay and some sorcery. Females, on the other hand, command the important positions in drow society. They are the priestesses of their dark goddess, Lolth (or sometimes Lloth), Queen of the Spiders. These females wield their tremendous goddess-given power mercilessly. Using the threat of intense punishment, they keep the males cowed and submissive. They are the top of the social hierarchy in the Underdark; they jealously guard their power against lowly males who might try to take that power away. Since drow females have greater power than males and are physically stronger and more intelligent as well, the drow have a difficult time believing that males can hold power in other societies. Thus, they do not believe that any threat mustered by males could seriously threaten the drow.
Despite their chaotic evil nature, the society of the drow is rigidly structured and divided. Social strata and classifications are virtually immutable. A drow can advance in her caste, certainly, but cannot advance beyond it. The chaotic nature of the drow is most evident when one seeks advancement—an advancement typically made through death.
Drow constantly seek to improve their position in society and in Lolth's eyes. If it comes at the expense of another's life, so much the better—that makes one less drow to challenge the newcomer, and it ensures greater security in the new position.
Drow have an abiding hatred of all things aboveground, but nothing draws their wrath quite like the good elves. The drow take any chance they can to destroy other elves they encounter. Even the few evil elves aboveground are seen as enemies, and the drow do not hesitate to betray such a one when he or she has served a purpose.