Symbolism, Imagery, Allegory
The "magic" barrel is actually an ordinary barrel where Leo keeps the cards of his clients:
"You wouldn't believe me how much cards I got in my office," Salzman replied. "The drawers are already filled to the top, so I keep them now in a barrel." (7)
Wait; scratch that. We're actually pretty sure the magic barrel is just a figment of Salzman's imagination. You sit on a throne of lies, Salzman! Leo visits Salzman's home and finds "no sign of Salzman or his magic barrel" (155). So unless the barrel is hidden in a closet somewhere, it probably doesn't even exist at all.
But even though we can discount the reality of the magic barrel, we can't discount its symbolic import. After all, it has a whole short story (and an entire National Book Award-winning collection) titled after it.
So what does it all mean, exactly? Well, barrels are usually pretty mixed-up places. A barrel is the anti- filing cabinet. Everything is mixed up inside barrels so what you pull out—a piece of candy, a pickle, or a name and picture of a girl—is a matter of luck. Or in this case, maybe a matter of fate.
Except—record screech—the characters in "The Magic Barrel" aren't bumping into each other on the street and finding True Love. They're being deliberately set up together by a professional matchmaker who doesn't use barrels, but instead has careful collated files of eligible bachelorettes and bachelors.
…Unless, of course, a rogue picture of a disowned, wayward daughter somehow gets into the mix and a hapless rabbinical student ends up falling for her. That really would be a pretty magical occurrence, wouldn't it?
…Unless, of course, a crafty matchmaker slipped a picture of his hauntingly pretty daughter in an envelope full of pictures of average-looking women and then gave that envelope to a lonely bachelor. The lonely bachelor would probably be intrigued, especially after being set up to fail on a few dates beforehand, right?
Dagnabbit, Malamud! You're too smart for us. You're also too ambiguous for us. Is this magical true love, or is it a wily old man doing what he does best? Is this a fateful meet-cute, or a cleverly orchestrated set-up? We'll never know, because the story leaves this (and all things, really) brilliantly ambiguous.