The climax of "The Open Window" occurs when Vera stares out the open window with "dazed horror" in her eyes. Framton Nuttel then feels a "shock of nameless fear" and quickly turns in his seat to peer in the same direction; in the twilight he is able to make out three figures who approach this window.
At the beginning of Saki's story, Framton Nuttel sits and talks to the niece of Mrs. Stappleton, his hostess, the girl asks if he knows anyone in the area. When Nuttel replies that he knows no one, the niece, Vera, realizes that she can tell Nuttel a tall tale and he will not know that it is not true. So, she spins a narrative around the open window and Mrs. Stappleton's husband and her two younger brothers who are out hunting and due to return as evening falls. According to Vera, the men were lost on the moor when they were "engulfed in a treacherous piece of bog" that terribly wet summer.
So, when Vera looks out the window in horror, Nuttel is frightened by her expression. Then, when he peers through the darkening evening and detects three figures, Nuttel is absolutely terrified and jumps up.
The climax comes in the last sentences of the story when Vera begins make up another story, this time about why Nuttel left so suddenly. The author writes, "Romance at a short notice was her [Vera's] specialty". The reader finally realizes that Vera also made up the story of the husband's death in order to scare Nuttel when the husband returns. We also discover how deceptive and cunning Vera can be, which is the whole point of the story.