Seymour Glass (a pun on self-reflection) is like Salinger, who saw heavy fighting in the Battle of the Bulge and may have suffered from post-war trauma.
Obviously, the main symbols are the bananafish, bananas, bananafever, and the bananahole. Two key passages are:
"Well, they swim into a hole where there's a lot of bananas. They're very ordinary-looking fish when they swim in. But once they get in, they behave like pigs. Why, I've known some bananafish to swim into a banana hole and eat as many as seventy-eight bananas." He edged the float and its passenger a foot closer to the horizon. "Naturally, after that they're so fat they can't get out of the hole again. Can't fit through the door."
Sybil said, "What happens to them?"
"What happens to who?"
"Oh, you mean after they eat so many bananas they can't get out of the banana hole?"
"Yes," said Sybil.
"Well, I hate to tell you, Sybil. They die."
"Why?" asked Sybil.
"Well, they get banana fever. It's a terrible disease."
Given that Seymor, a World War II veteran, shoots himself at the end of the story, the bananafish are analogous to him and other veterans returned from war. These men saw the horrors of war and the gluttony of death first hand. They were "ordinary" when they swam into the hole (war) but become gluttonous (full of greed) while inside and become trapped, diseased, and dead. So says an Enotes editor:
...the idea that Seymour is like the bananafish he describes: a man so glutted (with horror or pleasure) that he can no longer survive.
Not only can the hole be war, but it can also be a threshold, a coming of age from childhood to adulthood. Bananafish without bananas in their mouths are children, innocents. The fat bananafish with bananas in their mouths are corrupted adults. Banana fever seems much like materialism: mankind's obsession with "things" (money, land, status, bullets, tanks, dead bodies, a good job, a nice house, etc...).
The bananafish are much like the fish who are trapped beneath the ice in Central Park that Holden Caulfield worries about in The Catcher in the Rye. Those fish were a symbol of his dead brother Allie, who was forever frozen in time in Holden's mind.
As with Holden's pre-occupation with wanting to be a catcher in the rye, Seymour cannot fathom a child corrupted, seeing one of the bananafish with six bananas in his mouth. The corruption of children is the last bastion for Salinger's protagonists. No longer able to protect the young girl even at imaginary play, Seymour ends his life.
Other symbols include water, the hot sand, children, clothing, disease (banana fever), feet, and the gun.