The Society Of Assassins was a secret group of assassins.
Bruce Wayne became aware of the Society's existence at some point during his years as Batman. They lived by a strict set of rules, stating that any member of the Society who failed to kill his or her target would become a target, hunted by rest of the Society. But according to Bruce, none had ever failed.
Some time after Bruce passed the role of Batman to Terry McGinnis, the Society was commissioned by an international arms dealer, Fyodor Davic; he was scheduled for a trial a few days later, but it all hinged on the testimony of Defense Attorney Sam Young. Without the testimony, Davic would walk, so he arranged for Young to be killed.
Curaré, the Society's most skilled assassin, was sent to do the job. Her initial attempt was thwarted by Young's wife Barbara Gordon and Batman. After being reprimanded for her failure by the Master Assassin, she tried again, but her second and third attempts were foiled by Batman as well. She was taken into custody, and though she managed to escape fairly easily, the Society immediately began to hunt her for her failure.
The Society, however, underestimated Curaré, who had no intention of allowing herself to be killed. She struck back and began to hunt down her former comrades one by one, hitting each of them with a chemical that wiped their minds. After Kurima was dealt with, only the Master Assassin and Mutro Botha were left. Botha was sent to Gotham in order to enlist Batman's help in locating and subduing Curaré. Master Assassin was ambushed by Curaré when his plane was forced to make a landing.
Botha, who had witnessed the Master Assassin's demise over the phone, succeeded in contacting Batman shortly afterwards. He had anticipated Batman's refusal to cooperate, and to that end hid a powerful bomb in the city. With the city held for ransom, Terry reluctantly agreed.
Curaré unintentionally created a diversion when she attacked Maxine Gibson, who, having learned of the situation, decided to investigate Botha's apartment. With Terry out of the way, the assassin got through to Botha and used a pill to wipe his mind as she had done on the others.
Still seeking revenge on Batman, Curaré followed him and Max to the Gotham Museum of Armaments, where they had figured the bomb would be. Terry dealt with Curaré, and Max disabled the bomb. Using some of the armaments in the museum, Terry was able to disarm the assassin and handcuff her. She was taken into custody again, putting an end to the Society of Assassins.