Maureen Folan, a 40-year-old spinster, lives in the Irish village of Leenane, Connemara, in the early 1990s with her 70-year-old mother Mag, for whom she acts as caretaker. While Maureen is out, the Folan home is visited by Ray Dooley, a young man, who invites both women to a farewell party for his visiting American uncle. When it seems Mag is incapable of remembering this message, Ray writes it down for Maureen. As soon as he leaves, Mag destroys the note in the furnace. Upon Maureen's return, she admonishes her mother for depending on her as if she were an invalid; despite her bad back and burnt hand, Maureen thinks Mag is capable of doing more for herself. Maureen has already learnt of the party from Ray, whom she passed on her way in, so she punishes Mag for her dishonesty by forcing her to drink lumpy Complan.
Maureen, a virgin who has only ever kissed two men, buys a new dress and attends the party. She brings Ray's older brother, Pato, home with her. Pato is a construction worker who lives primarily in London, though he is unhappy both there and in Leenane. He reveals that, although he has barely spoken to Maureen in 20 years of acquaintance, he has secretly thought of her as "the beauty queen of Leenane" for a long time. She brings him to her bedroom. In the morning, Mag empties her bedpan into the kitchen sink, a daily habit that disgusts Maureen. Pato emerges from the bedroom and prepares breakfast for a shocked Mag, revealing that Maureen insisted he not sneak out. Maureen then emerges, dressed only in her underwear, and flaunts her intimacy with Pato in front of Mag. Incensed, Mag accuses Maureen of having deliberately burnt her hand by pouring hot oil over it, and then reveals that it is actually she who is legally responsible for Maureen after having signed her out of an English "loony bin." After Mag goes to find the papers that prove this, Maureen tells Pato that Mag burnt herself trying to cook unsupervised, but she admits that she truly did suffer a nervous breakdown while working as a cleaner in England, 15 years earlier, when she was unable to endure the teasing of her English coworkers. She claims Mag sometimes tries to tell lies about the past, thinking Maureen is unable to discern them from reality. Pato is sympathetic, telling her that his opinion of her is unchanged. However, when he urges her to dress herself for warmth, she becomes insecure about her appearance and throws a tantrum. Mag returns with the documents, but Pato ignores her, departing after telling an upset Maureen that he will write to her.
Some time later, Pato writes from London, telling Maureen that he is going to work for his American uncle in Boston, and he wants Maureen to come with him as soon as she can. The letter also reveals that he was unable to perform sexually when they were together, but he tells her that it was only because he had drunk too much. He also tells her that there will be a going away party for him. He sends the letter to Ray, with explicit instructions to put it directly into Maureen's hands. However, when Ray comes to the house, Maureen is out and Mag convinces him to leave the letter with her, playing on his resentment of Maureen for failing to return his swingball that fell in the Folan yard when he was a child and for snubbing him recently in the street. After Ray leaves, Mag reads and burns the letter.
On the night of Pato's farewell party, Maureen is aware of Pato's plans but assumes he is uninterested in pursuing a relationship. However, she tells Mag that it was she who ended things with him. When she continues to talk about the sexual encounter, Mag teases her and accidentally lets slip that she is aware of Pato's impotence. Seizing on it, Maureen tortures Mag with hot oil until she confesses the letter's existence and contents. Leaving Mag writhing on the floor, Maureen quickly puts on her dress and rushes out to the party.
She returns home after midnight, telling an unmoving Mag that she caught Pato at the train station before he left, and they recommitted themselves to one another. At the end of the scene, Mag slumps to the floor, dead. Maureen has bashed her head in with the poker.
A month later, Mag's funeral is held following an inquest that exonerated Maureen. Ray visits, bringing word from Pato. However, it soon becomes clear that Maureen imagined her reunion with Pato; he actually left by taxi without ever seeing Maureen. And now he has become engaged to a woman with whom he danced at the party. Maureen asks Ray to send Pato a message, "The beauty queen of Leenane says 'Goodbye.'" Ray leaves after discovering and seizing his lost swingball. Left alone in the house, Maureen puts on Mag's sweater, sits in her rocking chair, and adopts her mannerisms.