There's no real explanation for it, but getting a foul ball—or any other ball that finds its way into the stands—is pretty exciting. It's an unexpected physical reminder of an event. I have a foul ball I got from a spring training game on my desk. I don't know why I keep it—Hey, wanna check out my Jason Giambi foul ball from Spring training 2006?—but I do.
People just go to great lengths to secure a ball if they are close enough. When a pitch was fouled down the first base line during the fifth inning of the Mississippi State-Indiana game in the College World Series, a cute girl in pigtails was given just such an opportunity and she jumped at it.
Soon after she ripped it out of the hands of the adult male sitting behind her, the vultures descended and she divided her time fighting them off and egging them on. Elbows were everywhere and then, without warning, some poor kid got too close and got his cup of fruit punch elbowed right into his face and all over his shirt.
It might as well have been blood.
She continued waving the ball around while he bawled his eyes out. Every kid for him or herself.