The Elder Wand is the biggest, baddest wand there is—but symbolically, it's so much more than that.
For one, it's a big flashing red light that's screaming "Danger! Danger!" in Harry's general direction. Why? Well, because Voldemort has it. As Ollivander tells Harry, with the Elder Wand in Voldemort's hands, Harry's odds of surviving his upcoming epic battle with the Dark Lord are, um, quite low:
OLLIVANDER: He's after you, Mr. Potter. If it's true, what you say, that he has the Elder Wand, I'm afraid you really don't stand a chance.
So, yeah, early on, the Elder Wand kind of embodies just how steeply uphill Harry's battle is going to be.
The wand also becomes symbolic of the lust for power that Voldemort (and of course, many others) have, but Harry manages to avoid. Even Ron is tempted by the lure of this stupidly powerful wand when Harry ends up with it at the end of the movie:
RON: What should we do with it?
RON: Just saying, that's the Elder Wand. The most powerful wand in the world.
With that, we'd be invincible.
Harry doesn't seem to like Ron's enthusiasm about the wand—after all, this particular Hallow has already caused a couple of murders—so he destroys it immediately. Smart kid, that Harry.
And besides, Harry and the others manage to defeat the Dark Lord without the Elder Wand, right? Sure, the wand wasn't working properly for the Dark Lord because its allegiance was to Harry (who knew?), but still—if a bunch of kids can go up against a powerful wizard wielding that wand and win, wethinks there's something more powerful than any stinking Hallow.