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.