Abigail was a witch in Salem in 1692. She was under suspicion because her mother was a widow. She had begun a relationship with Obadiah Shaw, son of Reverend Hiram Shaw. The Reverend objected to his son's relationship with Abigail because of the suspicions that she was a witch (ironically, Hiram Shaw was actually the sorcerer supreme of his time).
After the mysterious death of Sarah Shaw (it was never revealed whether or not Abigail was actually responsible), Abigail was arrested for her murder and for witchcraft. Obadiah rescued her and the two fled. During the escape, Abigail reveals that she is a witch and reduces the townspeople to ash with a firebolt with the exception of Reverend Hiram Shaw.
It’s not known what happened to Abigail after this or whether or not Obadiah stayed with her after finding out she was a witch. With the name Harkness, she is almost certainly a relation to Agatha Harkness and possibly to Sebastian and Shinobi Shaw if she stayed with Obadiah.