What is the framing story of "The Open Window"?

This is a great question as you have identified one
important aspect of this darkly humorous short story. A framing narrative or framing
story is a literary term we apply to any text which contains a story within a story, or
where in the middle of the text, one character tells another character a different
story, and we go through different levels of narration. Thus it is that famous novels
such as Wuthering Heights and The Turn of the Screw feature framing narratives, because
we start of with one narrator who then quickly narrates what another character has
narrated to him, if you understand that.

Let us look at
"The Open Window" as an example. The narration starts off focussing on Mr. Framton
Nuttel and his meeting of Vera. This is the framing narrative, because very quickly we
are told the story within a story from Vera, about the supposed fate of her uncles. Then
we have the frame again before Vera tells another quick tale to explain Mr. Nuttel's
hastly departure. Framing narratives literally "frame" or go around the story within a
story.