Proctor is identified with the quality of "lust" in his private conversation with Abigail. Though he refuses her advances, his former affair with her is exposed.
Prior to the action of the play, Abigail was a servant in Proctor's house, as Mary Warren is during the play. She is "released" from her duties at the Proctor house when Elizabeth finds out about the affair.
The town wonders why Abigail was fired, as Parris discusses in the opening scene of the play, though Abigail feigns innocence.
When she speaks with Proctor in the first act, the truth of the matter becomes clear. Proctor and Abigail did indeed have an affair. He was once overcome by lust.
Yet, Proctor has severed his ties to Abigail and attempts to control his feelings for her.