Symbolism, Imagery, Allegory
We'll say "the Winchester," even though the same principle applies to guns in general. Jack loves guns. They make him feel big and strong, and more in control of his ridiculously out of control life:
I needed that rifle, for itself and for the way it completed me when I held it. (3.2)
"Completed," he says. Like it's a part of him, the same as a leg or an arm. That's pretty important: maybe even more important than parts of his real anatomy. He uses it to assert control over his life, most notably when he points it at passersby out the window:
I sometimes had to bit my lip to keep from laughing at the ecstasy of my power over them. (3.7)
Yikes. He's almost crazy in these circumstances; when someone laughs about perceived power that way, it's probably someone who has very little power in any other form. Hence, gaining some is the most important thing in the whole wide world.
Sadly for him, but happily for the victims of his shooting-spree-that-never happened, his power is an illusion. He can't actually use it, least he kill someone and go to jail for the rest of his life (which would make for a much different, more shiv-intensive story). Even when he gets away with it, he pays for it, like when he shoots the squirrel and "blubbered again in bed that night." (3.11).
It's a tough bind—he loves the illusion of power, but can't handle the reality—and it gets worse when Dwight shows up. (You could say that about a lot of things. Dwight's just that kind of guy.) But it comes out particularly in regards to the rifle, which Dwight first refuses to let him use at the turkey shoot and then sells without his permission to buy him Champion. Dwight takes ownership of the gun, which pretty much symbolizes his claim to Jack's perceived power. Stupid Dwight. Of course, Dwight can't use that power effectively either. "'That,' he said, 'is the most stupidly constructed firearm I have ever seen, bar none.'" (8.58) This, despite the fact that both Jack and Jack's mom can use it just fine. Dwight's just using it to excuse his own lack of power, and it's easy since the Winchester can't, you know, make an argument.
Power in the rifle really is an illusion, whether Jack's playing future mass murderer with it, or Dwight's trying to show how much control he has over Jack. You can't use it (not without lots of cranky cops getting involved), but it makes you feel like you can. That's a tough feeling to shake, even when its phoniness jumps up and down on you multiple times.