In Jack Finney's short story "Contents of the Dead Man's Pocket," in the lines in question, Tom has just overcome his fright enough to bring himself to cross back from the ledge of the one building where the paper had come to rest back to the ledge of his own building. He has also brought himself to start very slowly edging his way along his own ledge back to his window sill by taking "dozens of tiny sidling steps" with his "chest, belly and face pressed to the wall." As he moves along, he uses his fingers to feel along the brick facade of the building, which helps him keep moving in the right direction and helps him maintain his handhold on the bricks.
However, in the lines in question, he also makes the mistake of letting one "fraction of his mind" realize he is going to fall, which makes him panic. As he panics, he starts taking steps more rapidly without patiently feeling for what he's doing. As he keeps scrambling along the brick, he keeps letting his hands slide forward until his "left hand slid onto not brick but sheer emptiness, an impossible gap in the face of the wall," which makes him stumble. The "sheer emptiness" is explained in the next clause--the emptiness is a "gap" or hole. By "gap," we can assume that he simply means there is a large space in the brick's mortar caused by wear and tear. He is probably also using hyperbole, meaning exaggeration, to describe the gap in the facade because it startled him so much. However, had he been going slow enough, he would have been able to feel around the gap and would not have lost his balance.
As a result of being startled by the gap, he stumbles, staggers, and starts to fall but breaks his fall by clawing at the glass and wood of his window pane and window sill.