John Nash realizes that he has hallucinations at the climax of the film. In this scene, the setting of the climax is Princeton, New Jersey in 1956. Nash takes his baby up the stairs for a bath while his wife goes to do laundry. Alicia does not normally trust John alone, but after a long moment of seeing the worry in her face, he says, "It's okay," to assure her that she can trust him.
As his wife hangs the laundry, an ominous storm whips up, during which time Alicia is drawn by wind-flapping doors to check the shed. There, she finds a horrific sight: John has been deep in his paranoid delusions again, pinning paper clippings to the walls in an effort to solve a conspiracy that is not real. Realizing her husband cannot be trusted, she runs to the house and upstairs to find her son nearly drowning in a filling bathtub. John tries to calm her worry by saying, "Charles is watching him," but she caresses her baby and shouts, "There's no one here" a couple of times.
The scene culminates into a high-suspense moment as Alicia calls Dr. Rosen. As she calls, Parcher (a character who leads John's conspiratorial hallucinations) shows up with a gun, threatening to shoot Alicia while she is on the phone. Nash, thinking he is rescuing his wife, roughly gets between her and the gun, and she falls onto the floor, still holding the baby. She shouts at John to get away from her and gets into the car with their child to leave. Parcher then draws his gun on John, threatening to shoot him if he does not "take care of" Alicia—that is, kill her for being a threat to the high-profile mission. Charles appears and encourages John to do as Parcher says. Then Marcee, the hallucination of a little girl, grabs John's hand in a comforting way and looks up at him.
This is the true moment of recognition and clarity for John, as suddenly he has a flashback to college and realizes this little girl has never aged. He runs out to the car, stopping it as his wife is pulling away.
She never gets old. Marcee can't be real. She never gets old.
Through logic, Nash was able to overcome his hallucinations and reason that all the people who were so real to him for so many years were not real after all. This is the turning point for John Nash, a moment of clarity that leads to a brighter future.