Dave feels so manly when he holds his dinky pistol that the thing might as well be a bazooka. This makes perfect sense since Dave only buys the gun in the first place to feel as macho as the Overly Manly Man. After being bullied all day in the fields, Dave is convinced that his coworkers "couldn't talk to him as though he were a little boy" (1) if he owned a gun. With this in mind, it's clear that the pistol represents Dave's masculine ideal. That it's a phallic symbol doesn't hurt either.
On a simpler level, however, Dave desires the gun because he wants power, plain and simple. For him, this feeling centers around Mr. Hawkins, the rich white plantation owner who runs the farm where Dave works. Hawkins is the most powerful man that Dave has ever met, but with the gun in his hand Dave "could [...] kill anybody, black or white" (114). Although Dave doesn't consciously understand that Mr. Hawkins holds more power solely based on his whiteness, he does understand that Mr. Hawkins is more powerful than anyone else he knows. And with the gun, Dave senses that he can upend this power dynamic.
Interestingly, Dave's relationship with the gun changes over the course of the story. Dave is an awful shot at first, closing his eyes and losing his grip on the pistol when he fires it. By the end, however, he's able to fire with his eyes open and "the gun [...] still in his hands" (209). That's an improvement, yes, but it's also symbolic.
Dave's improving gun skills represent his growth over the course of the story, from teen without agency to a young man capable of making his own decisions. You might not agree with his decisions, but that's besides that point. Either way, Dave's growing proficiency with his pistol mirrors his personal growth from boy to man. So much so, in fact, that in using it, he sets in chain the sequence of events that culminates in him heading off into the world on his own.