What is the role of setting in "The Open Window"?

There are a few different aspects to the setting in this story. The first point to note is that the residence that the protagonist, Framton, arrives at, is described as a "rural retreat" and a "restful country spot." This seemingly idyllic setting lures the reader, and Framton, into a false sense of security. Accordingly, the macabre story that the niece relates seems all the more sinister because it seems so out of place.
Within the niece's story, we also have the settings of the moor and the marshes. Moors and marshes are settings often used in ghost stories (The Woman in Black, Wuthering Heights) and evoke a sense of isolation and eerie, untamed wildness.
Finally, the time of day at which Framton sees the three ghost-like figures walking towards the open window is also significant. Saki sets this moment in "the deepening twilight." Twilight in literature is often used to evoke an ominous atmosphere, because it is the time of the day when light is fading and darkness is taking over. Therefore, twilight is the perfect time (from a writer's perspective) to have the three ghostly figures return. It suggests that they are figures of the night, and of the darkness.

The setting of "The Open Window" is absolutely crucial in conveying Saki's ironic intent. The story takes place in a large, comfortable, Edwardian middle-class house in the depths of the English countryside. This is not a place where we'd expect anything especially horrific or terrifying to take place. That is, unless you happen to be Framton Nuttel, of course. He's staying in the countryside on doctor's orders, hoping to find a rest cure for his nervous disorder.
On the face of it, it would seem that a visit to the Sappleton residence could be just what the doctor ordered. And when Framton is introduced to a rather normal, ordinary-looking young lady, there doesn't appear to be anything about this social visit that might remotely damage his poor, frayed nerves. The apparently calm, tranquil, thoroughly respectable setting of "The Open Window" lulls both Framton and the reader into a false sense of security which makes Vera's gruesome shaggy dog story all the more effective.