Darla is one of the oldest Vampires seen on the show. As a human, she lived in the Virginia Colony as a prostitute, and developed Syphilis. In 1609, when she was near death, The Master came and sired her. He took her back to Europe where she was glad to become part of his Order of Aurelius.
In 1753 Darla sired Angel. When Angel had no interest in joining The Master's order, Darla left the order with Angel to do their own thing. For one hundred years they lived together, traveling the world, creating death and destruction where ever they went.
Angel sired Drusilla in 1860, who sired Spike in 1880. These two were not hunters in the same was Angel and Darla were, and Darla did not like them very much. When Angel was cursed with a soul in 1898, Darla was stuck with Dru and Spike. She tried to get used to it, and she tried to get Angelus back, but she was unable to, and eventually rejoined The order of Aurelius.
In 1927, in Sunnydale California, The Master tried to open The Hellmouth and was trapped in it. Darla and the rest of the order were forced to bring him food, as there was no way to get him out. In 1996, a ritual called "The Harvest" was performed in a attempt to free The Master. Darla helped, but the plan was stopped by The Slayer. Darla continued to work for The Master, in hopes of finding a way to free him. At this time, she discovered that Angel was living in Sunnydale. She went to him, tempting him to come back to The Order with her. This did not work, and The Slayer got involved. In the end, Angel killed Darla to save The Slayers life.
In 2000, Darla was resurrected as a human in a very complicated ritual arranged by Wolfram and Hart, a law firm in LA. This law firm is run by mortals, working for very powerful demons. Because Wolfram and Hart defend some very evil demons (Such as Russell Winters), Angel had become a big problem, as he would make life very hard for the demons. Darla was resurrected in an attempt to make Angel turn back into Angelus. For many months, Darla worked on Angel, first using magic to make him dream of her, and later making Angel look crazy, by having him tell everyone she was a vampire, even when she was able to stay in the sunlight since Wolfram and Hart brought her back as human. Angel was eventually able to expose her, however.
Not long after that Darla was beginning to feel guilt, now that she was human, she had a soul, and it started to drive her crazy. She went to Angel, begging him to turn her into a vampire, to get rid of the guilt, but he wouldn't. Matters were complicated further when Darla found out, she was still suffering from the Syphilis that almost killed her as a human back in 1609. Angel still refused to change her, and followed her around, making sure she would not get some other vampire to change her. In the end though, one of Wolfram and Hart's lawyers, Lindsey MacDonald, who had fallen for Darla, arranged for Drucilla to come and sire Darla herself.
Dru turned Darla without a hitch. Darla was now wanting revenge on Wolfram and Hart for bringing her back as human, and using her. She and Drusilla did this by going to a Wolfram and Hart gathering, and killing everyone there but Lindsey, and his sometimes adversary Lilah.
After Drucilla left, Darla briefly worked with Lindsey, in an continued attempt to turn Angel. They were able to make Angel feel his quest to help people was futile, and got him to have sex with her. The result was unexpected, this did not cause Angel to turn, and as a result, gave him new hope. Defeated, Darla left LA.
Darla was interesting because she is one of the oldest vampires. Before being resired, she was very strong, and like Angel, resistant to injury. She was stabbed in the stomach and hardly phased. Her face also recovered quickly from being burned by holy water. It's hard to know if Darla will lack some strength because she is really a 'new' vampire again, and not an aged super vampire any longer. Darla also shows an alternative to Angel, when she gained a soul, she did not feel guilt right away. This is because Darla as a human, had much less of a conscience. In the end, it did get to her however. Another thing about Darla is that she's the only vampire we've seen be resurrected. Because Darla left no bones like The Master, her resurrection spell was incredibly hard to do, it's only because of Wolfram and Hart's resources that she was able to be resurrected. Bringing a vampire back is incredibly hard work, which is why we rarely see it.