Rosemary was a Receiver-in-Training, the daughter of the Giver, who imparts his knowledge to Jonas, his new trainee.
In Chapter 18 Jonas asks the Giver about the concept of release. The Giver tells Jonas that he cannot be released until the new Receiver is named. The Giver tells Jonas,
"I know that. They hammered out those rules after the failure ten years ago."
This rule on no release came about after a Receiver-in-training named Rosemary abruptly asked for release after having been given memories of pain. The Giver tells Jonas that he loved Rosemary, but he had to impart such memories as loneliness to her. "She appeared stunned at its end." Then, one afternoon, Rosemary kissed the Giver on the cheek and left the room, and he never saw her again.
When Rosemary was released, her memories were also released into the community and the people were traumatized by the sensations of pain because they were unequipped to handle them. As he listens, it becomes clear to Jonas that the Giver has been greatly affected, but Jonas still does not fully understand release until he watches a video that shows his father releasing an infant. This new knowledge greatly affects Jonas, causing the Giver, who has been deliberating upon the ills of his community, to decide that memories must come back to the community because there are terrible flaws to their lives, one of them being euthanasia. It is then that the Giver reveals to Jonas that Rosemary injected herself, committing suicide, and that she was his daughter.