Character Clues
Character Analysis
Physical Appearance
The Magic Barrel" uses physical appearance to tell us pretty much everything we need to know about characters' backgrounds, personalities and states of mind.
Salzman is "a skeleton with haunted eyes," (116) which speaks to his lack of success at work, his care and worry, and—oh yeah—the whole "my baby girl is going to hell" thing. Similarly, we get his eagerness to find a nice girl for Finkle with his "hungry" expression (60.
Finkle, for his part, reveals much of his subsequent despair and trouble when "His beard darkened and grew ragged" (115). No need for fancy psychology or lengthy mental interrogations: the beard tells all.
Even Stella, who doesn't appear until the very and end who never gets a chance to speak on her own, gives us a very direct impression of her state of mind from her eyes "filled with desperate innocence" (201). Like the rest of the story, the physical descriptions are very brief: usually little bite-sized two- or three-word snippets. But they deliver all that we need to know about who these people are and what they're going through.
Occupation
Leo's a rabbinical student. Salzman is a matchmaker. Neither of them makes a lot of money.
Once we know these things, we can see a lot about what matters to them. Leo's lives "in a small, almost meager room, though crowded with books" (1) while Salzman's apartment "was sunless and dingy, one large room divided by a half-open curtain, beyond which he could see a sagging metal bed" (155). We can see that, to Leo, what's important is learning and that Salzman's matchmaking business isn't exactly making him a rich man.
Family Life
Leo explains that "his home was in Cleveland, and that but for his parents, who had married comparatively late in life, he was alone in the world" (3). This suggests that he is someone looking for his place in the world, and who might need a matchmaker solely because he doesn't know anybody else who could introduce him to a nice girl.
As for Salzman: he's got himself a wife and a daughter that he has disowned. His testy relationship with his daughter may explain why he's a matchmaker; it could be a way of correcting what went wrong by bringing young people together… or it could be a sneaky way of getting her marry a soon-to-be rabbi that has "concluded to convert her to goodness" (189).