Alienation is woven throughout the plot of The Crucible and involves many of the characters. Tituba is alienated from the town of Salem because of her race and the perception that she is a witch. Abigail is alienated first from the Proctor family and then from Salem as a whole because of her lies. Mary Warren is alienated from the other girls because she threatens to expose the truth. John Proctor is alienated from his wife because of his affair and then alienates himself from his own faith and religion in response to the town's accusations. Mr. Hale is alienated from his own sense of truth and reality because of what he observes in the town. These are just few of examples of alienation throughout the play.
Alienation occurs when a person withdraws himself or herself or their affections from something or someone to whom they used to be attached. Therefore, John Proctor becomes alienated from his wife when he chooses (prior to the play's beginning) to have an affair with another woman, and he later becomes alienated from that other woman -- Abigail Williams -- when he severs their connection and ends their relationship. Elizabeth Proctor is certainly alienated by her husband's choices, and we see her withdrawal of affection when she merely "receives his kiss" in Act II, and Elizabeth and John's ability to communicate effectively as a result of this alienation, perhaps, prevents John from telling the truth that he knows before it is too late.
Abigail is likewise alienated by John's choices, and it seems probable that this alienation prompted her to manipulate the witch hysteria so that she could accuse Elizabeth, eliminate her, and get John all to herself. Therefore, the alienation that occurs among these three characters as a result of John's initial indiscretion (a sin, for them) is actually a really important aspect of the plot.