Dark Willow is the name given to the evil alter-ego of Willow Rosenberg following the death of her lover Tara, which coupled with her addiction to powerful and dangerous magic ultimately caused her to lose her sanity and become a major antagonist to the team as she sought to end her suffering via bloody vengeance against the "Trio" she viewed as responsible for Tara's death then destroy the world.
"Dark Willow" is considered the true "Big Bad" (Buffyverse term for Main Antagonist) of season six with Warren and his gang being catalysts to unleash her rather than actual threats (though Warren arguably became a genuine threat). In the Buffy Season 8 comics, her dark side returns in the 23rd Century and is known by her new alias "The Madwoman."
History
First Dark Emergence in the 21st Century
The history of Willow before becoming corrupted is a fairly complex one but she had always been a fairly sweet-natured individual, starting off as a rather socially-awkward individual she grew in confidence as she grew older and somewhat famously became engaged in a same-sex relationship with Tara: the two of them becoming powerful witches.
Sadly it was Willow's involvement with witchcraft that would become her undoing as she was unable to truly limit herself, drawn towards powerful and forbidden sorcerery she had always had a problem with magic similiar to addiction, however with help from her friends she usually overcame her dark desires.
However during the course of season six Willow's addiction became far worse than before and she endangered her friends on several occassions, to the point she even broke her promise to Tara to stay away from magic from a week (trying to erase her memories of the effects) - eventually Willow's behavior caused Tara to dump her.
Willow continued to abuse her talents, going as far as seeing an evil warlock known as Rack - who was basically a supernatural drug dealer - eventually Willow was forced to realize the effects she was having on others when a demon summoned by one of her spells hospitalised Dawn, who she was meant to of been looking after.
After Willow promises to never use magic again (or at least not until she can control herself) Tara decides to forgive her and the two resume their relationship - sadly Willow's happiness was short-lived as an increasingly psychotic Warren decided to exact his revenge on Buffy via opening fire on the group with a gun: injuring many and killing Tara with a stray bullet.
Overcome with grief and anger Willow transformed into "Dark Willow" and began her vengeance - tracking down Warren and torturing him before flaying him alive using magic, she then proceeded to absorb the powers of Rack before going after Andrew Wells and Jonathan Levinson despite the fact they were not responsible for Tara's death (in fact unlike Warren these two were not truly villains, rather misguided and rather foolish) - nevertheless Willow pursued them relentlessly and clashed with her former friends as a result.
When Giles attempts to stop the madness via battling Willow with the power of an English coven she simply steals his power as well, in the process she grows so powerful that her grip on reality is completely lost and she seeks to end the world to stop the unbearing pain her mental anguish is causing her.
However as Willow began to summon the power of the apocalypse via the effigy of the demon Proserpexa she was confronted by Xander, he proceeded to tell Willow that no matter what she became or what she did he would always be her friend and as she attacked him he simply told her repeatedly that he loved her - eventually Xander's actions made an impact and Willow broke down, finally ending her torment as she cried into her friend's shoulder.
Following the events of "Dark Willow" things began to go back to normal for Willow but memories of what she had done and how she had harmed her friends continues to haunt her and those who knew her..
The Second Coming of Darkness in the 23rd Century
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Dark Willow returns in a possible future
Willow remained youthful for centuries and eventually resumed her "dark" appearance of black hair and veins. Approximately two hundred years into the future, Willow was located in Haddyn—otherwise known as Manhattan—and was the one responsible for bringing Buffy Summers through time. Willow was allied with Harth Fray, the vampiric brother of current Slayer Melaka Fray. Harth considered Willow to be a "madwoman" but believed her claims that Buffy's presence in the future would cause that future to exist. However, Willow also manipulated Melaka into viewing Buffy as her enemy, telling her that if Buffy returned to her own time, Melaka's time would cease to exist. Melaka and her sister Erin captured Buffy, who was shocked to see what her friend had become. When Harth arrived at Melaka's home, both parties learned that Willow was lying to one of them. Buffy managed to escape and fought her way across Haddyn to get to a rift in time and return to the present, battling Melaka in the process. When Buffy arrived at the rift, Willow stood in her way. Before Willow could reveal her true agenda, Buffy stabbed and killed her friend with the Scythe, which it has been hinted was Willow plan all along to have a best friend end her sad existances. At that point, present Willow—blindfolded so as to avoid seeing the future—grabbed Buffy and pulled her back in time.
Traumatized by the sights of Melaka's time, Buffy began to express concern over how much she relies on Willow's powers, fearing that she may eventually go overboard again if she was pushed too far.