The open window is what Vera seizes upon to trick the poor unsuspecting Framton Nuttel when she is left to entertain him by herself while her aunt is preparing herself. Note how she uses it to weave an elaborate story that the gullible Mr. Nuttel completely swallows:
"You may wonder why we keep that window wide open on an October afternoon," said the niece, indicating a large French window that opened on to a lawn.
She goes on to tell Mr. Nuttel how the window is kept open for the supposedly dead husband and two younger brothers of Vera's aunt to return, completely setting the stage for their actual return and the hasty departure of Mr. Nuttel.
However, more than this, the open window seems to be related to one of the possible messages of the short story. The window in its very openness reflects both Mr. Nuttel and Vera's aunt and family in their willingness to be deceived and misled by somebody with Vera's skill and perspicacity. It seems that the story contains a warning - are we "open windows" to those such as Vera, to be played with and tricked and deceived, even in jest, or are we able to discern the truth?
The open window leading from the big living room to the outdoors provides unity of place, to use one of Aristotle's terms. In plotting the story Saki wanted to have the visitor Framton Nuttel terrorized by the arrival of three men carrying guns, three men whom he thought to be either ghosts or "living dead," zombies. Saki decided that he could not have the three hunters return through a back door and get rid of their guns and dead birds before entering the living room, because that would not elicit the desired effect on Framton Nuttel. The open French window was essential to the story. That was why Saki titled his story "The Open Window" and used so many words to explain why it was open and what Vera and her aunt were expecting to see. When Vera first greets Framton, she says:
"You may wonder why we keep that window wide open on an October afternoon."
It is actually the reader who may wonder why they keep the window wide open, and Saki, through Vera, has to explain as best he can. The reader may also wonder why these men in their wet clothes and muddy boots don't customarily reenter the house by a back door and take off their boots before coming into the living room for tea. Saki had to make it plausible that the men should be so careless. The reader is led to believe that that's just the way upper-class country gentry behaved. They even brought their muddy spaniel straight into the living room, and the dog probably spent much time lounging on the furniture. The three men and their dog are not only going to come straight into the living room, but we the readers are led to believe, by both Vera and Mrs. Sappleton, that they always come straight into the living room through the open French window, regardless of how wet and muddy they might have become. Note what Mrs. Sappleton says to Framton when she sees the men outside.
"Here they are at last!" she cried. "Just in time for tea, and don't they look as if they were muddy up to the eyes."
Moments earlier she makes a similar remark:
"I hope you don't mind the open window," said Mrs. Sappleton briskly; "my husband and brothers will be home directly from shooting, and they always come in this way. They've been out for snipe in the marshes to-day, so they'll make a fine mess over my poor carpets. So like you men-folk, isn't it?"
Mrs. Sappleton has led a sheltered life. She assumes that Framton must be interested in killing birds and capable of tracking mud all over people's floors because she takes it for granted that men are all alike. Three men and a dog will be tracking mud all over her carpets and hardwood floors, but she doesn't seem perturbed. Saki will have to persuade the reader that the three men don't care about making a mess and Mrs. Sappleton doesn't care either, because Saki wants them to enter the living room directly from the outside. That is the only way that Framton could see them heading straight towards him carrying their guns.
Once Saki thought of having the men return through an open French window, he used it to inspire Vera to make up her story. It was essential to Vera that her aunt should be in the habit of waiting for the men every evening at tea time and that she should be expecting them to enter through that window. Saki still doesn't explain why the French window, which is like a floor-to-ceiling door, should have to be standing open. The men ought to be capable of opening the window for themselves. It can't be that warm inside the room if the men are returning all wet and muddy and it is getting dark outside. A French window is made mostly of glass. It is more of a window than a door, but it can be used as a door. The window really did not need to be "open" at all for Framton to see the men approaching, but the fact that it is open is needed to establish that this is the way the men will be entering the house. The fact that it is open makes their approach more frightening to poor Framton because it eliminates the faint possibility that the window might be locked.
Vera's story is especially effective because these three men are avid hunters. So all three are carrying guns. This makes them infinitely more frightening to poor Framton.