Symbols in Bernard Malamud's "The Magic Barrel" abound. First, a symbol is...
A word, place, character, or object that means something beyond what it is on a literal level.
We are surrounded by symbols in our daily lives: a dove symbolizes peace; hearts and roses both symbolize love; black symbolizes evil or death. In literature, sometimes finding symbolic meanings is more difficult, but adds an entirely new hidden meaning to the story.
One symbol in the story may be Salzman's "black, strapped portfolio that had been worn thin with use." The story's title has "magic" in it. Salzman appears in the hall of Leo's building out of the darkness. He promises to arrange a marriage for Leo from cards he pulls out of the bag: the bag, like a magician's black hat, could symbolize magic.
Eyes are referred to many times throughout the story. Salzman has "mournful eyes." Stella's eyes are "filled with desperate innocence." Eyes are said to be "windows to the soul." We might assume that the eyes in the story symbolize truth, for Leo seems to find feelings projected through Salzman and Stella's eyes to reflect the truth of their inner feelings.
Fish are also referred to in a variety of ways. When Salzman arrives at Leo's apartment the first time...
He smelled frankly of fish.
When he visits Leo again, he brings his lunch (perhaps a reference to the Biblical miracle of loaves and fish)...
...a hard, seeded roll and a small, smoked white fish.
Salzman's wife is described to almost look like a fish:
"No." Her mouth, though left open, offered nothing more.
As he looks around Salzman's apartment...
An odor of frying fish made Leo weak to the knees.
Salzman arrives again at Leo's home, and the young man fixes Salzman something to eat: a cup of tea and "a sardine sandwich." And when Leo runs into the old man at a cafeteria on Broadway, he was "sucking the bony remains of a fish."
Fish have a great deal of religious significance in terms of miracles in the Bible. Jesus performed the miracle of the loaves and fishes, feeding five thousand from the lunch of a young boy. Several of the disciples were fisherman. When Jesus first called the apostles, the first miracle they saw was when he told them to cast their nets on the other side of the boat: there are so many fish that their nets broke. Perhaps "salz" infers that Salzman is a man with the power to perform miracles. (Leo thinks he could make it snow if he wanted to.)
Salt is also reference in the story, though indirectly. Salt's importance can be seen in...
...symbolizing immutable, incorruptible purity...
"Salz" in German means "salt." Historically, salt was used in trade as a valuable commodity; to cleanse the ground of blood where a battle had taken place; it preserves meats (and fish). It is associated with magic in many cultures. Perhaps the most common belief is that a circle of salt will protect one within the circle from evil. Perhaps Salzman's character is associated with magic and he is able to protect his daughter from evil—finding Leo to save her. He may have a purity of spirit.
The color of red is often symbolic of prostitution, hence the term "red light district" for an area of town inhabited by prostitutes. White is symbolic of purity. At the end, Stella wears a white dress with red shoes, but Leo imagines momentarily that the dress is red, and the shoes, white. The red dress may symbolize her past and the white dress, her desire to start anew.