“The Leap” is told by the daughter of an interesting woman. ​​The narrator begins by describing her mother, one half of a former blindfolded trapeze act called the Flying Avalons. Though her mother, Anna, is now blind and never even talks about her days working for the circus with her first husband, Harold Avalon, she retains much of the grace she must have possessed then. She has moved back in with her mother after her father’s recent passing and her mother’s declining eyesight. The narrator says that she owes her mother her existence three times over. 

First, during Anna's act one day long ago, a huge thunderstorm came without warning, and lightning struck the main tent pole at the circus. The trapeze Harry (her husband) was swinging on fell down, and he plummeted into the crowd and died, along with two others. Anna might have been able to grasp his ankle, potentially following him down into death, but she made a split-second decision to save herself and her unborn child (she was seven months pregnant, unbeknownst to anyone in the audience). She remained nearly uninjured herself, save for major burns on her hands when she grabbed a lightning-hot pole to save herself from the fall. Ironically, it was the rescuers who accidentally broke her arm and tugged on a loose tent pole that knocked her unconscious. Despite her heroic efforts, however, the child was stillborn a month or two later. This is a story the narrator knows largely through historical records and newspaper articles because Anna does not revisit this period of her life often. Harry was buried in the circus cemetery with his family, and Anna’s stillborn child was buried a short distance from the narrator’s childhood home. The narrator used to visit the grave, considering this baby to be an “incomplete” version of herself; not a lost sibling but rather a precursor to her existence. 

The second time the narrator credits her mother with her existence is when Anna fell in love with the doctor who set her arm in the hospital after the accident. The doctor—the narrator’s father—specialized in injuries that occurred due to parachuting accidents. This doctor taught her to read and write, even buying her first book. Though the pair of them could have moved anywhere, Anna wanted to remain there because her child had died and was buried there, so they moved into his family's farmhouse and stayed. The narrator is somewhat perplexed by this choice that her parents made. She cannot imagine why her father, who wanted to leave the town in general, and her mother, who experienced the death of both her husband and child, would stay.

The third time occurred when the narrator was seven years old. Their house caught fire, and the one set of steps up to the narrator's room was in flames. The narrator did as she'd been taught, touching the doorknob to feel its heat, rolling up a rug to place under her door, and waiting for rescue. But it was clear to Anna that no rescue would be possible. So she stripped off her dress, climbed a tree, shimmied out onto a too-small limb, leaped the distance from its tip to her daughter's window, and saved the little girl herself. The narrator can sometimes still smell the smoke as she remembers that night.