What is the "sheer emptiness" Tom encounters in "Contents of the Dead Man's Pocket"?

The literal answer to this question is that Tom encounters the "sheer emptiness" of open space where he was expecting to feel a continuation of the brick wall that he was clinging to:

"Then his moving left hand slid onto not brick but sheer emptiness, an impossible gap in the face of the wall, and he stumbled."

Right then, he's edging, crablike, along the wall, trying to reach the paper that flew out the window with the breeze. That's the only time that the phrase "sheer emptiness" appears in the story. In fact, that's also the only time we see even the word "emptiness" by itself.

But more to the point, Tom encounters a sheer emptiness in his own life, brought on by his focus on his work to the exclusion of enjoying his marriage. He's missing a potentially fun and meaningful evening out with his wife just so he can stay home and work on some research for his job at the grocery store. And when the sheet of paper containing his notes flies out the open window, he foolishly chases after it; the dangerous excursion out onto the ledge of the apartment building makes up most of the story, and Tom nearly gets himself killed.

Eventually, he's trapped outside on the ledge, unable to reopen the window, and wondering if he'll lose his balance and die before anyone can rescue him, when he starts emptying his pockets of everything except that paper of notes that he was able to grab. He throws away meaningless letters and useless coins. And there's nothing else in his pockets that would help people identify his body if he were to fall and die on the concrete far below. Tom is empty, then, in a figurative way as well: he's wasted his time at work, and all that people will find on his dead body is an "incomprehensible" sheet of notes. Even this project he's been working on doesn't matter, he realizes.

Let's take a look at the passage where Tom realizes all this, when he understands how he's been living his life in an empty way:

He wished, then, that he had not allowed his wife to go off by herself tonight--and on similar nights. He thought of all the evenings he had spent away from her, working; and he regretted them. He thought wonderingly of his fierce ambition and of the direction his life had taken; he thought of the hours he'd spent by himself, filling the yellow sheet that had brought him out here. Contents of the dead man's pockets, he thought with sudden fierce anger, a wasted life.

Happily, we realize that Tom has changed and that he will change the way he lives his life from now on when he breaks the window, safely reenters the apartment, and allows even the yellow paper to fly back outside as he laughs and heads out to join his wife. He's going to fill the emptiness of his spirit by recognizing what's really important to him: his wife, not the potential money he might make by being recognized and promoted at work.