The asteroid belt of the Solar System isn't of uniform density - it has gaps at odd locations within its interplanetary domain. Astronomer Daniel Kirkwood first documented these unexpected vacancies in the Mars-Jupiter orbital region back in 1886. Following is an explanation for the gaps that bear his name.
(Part of the lure of science is the discovery of something new, and of having your name associated with some aspect of the universe. Poor Kirkwood is now known for absences - for gaps - for nothingness. Just how existential is that?!)
Er...ahem. Back to the asteroids. The best explanation for their absence involves the phenomenon of orbital resonance. An asteroid located at the radius of one of these gaps would have an orbital period of some whole number ratio of that of Jupiter. So every few years (the number depending on which particular gap we're talking about), the asteroid would be in the same place relative to Jupiter, by far the most massive planet in the Solar System. For most asteroids not occupying one of these depopulated zones, Jupiter's gravitational effects sum to very nearly zero, but the perturbations effected by Jupiter on a body in one of the Kirkwood gaps are nontrivial.
To give the simplest case, consider an asteroid which orbits twice for every Jovian orbit: it would occupy the 2:1 gap. Every time Jupiter completes its way around the sun, this asteroid would be at one of two places. Gravity acts as a vector just like any other physical force - Jupiter's going to pull on that asteroid in the exact direction of the line separating them. If the asteroid weren't in a resonant orbit, the direction of the vector would be essentially random, and these forces would cancel over the course of many periods. But our supposed Kirkwood resonant asteroid isn't so lucky. Since it's in the same place relative to Jupiter over and over again, the long-term effects of gravity add up. Its orbit soon becomes unstable (soon on this scale could mean thousands of years, but nonetheless...) and the asteroid breaks free to collide with other asteroids and generally cause cosmic havoc. Maybe it crashes into a planet - maybe it restabilizes in another orbit - maybe it leaves the Solar System entirely. But the important point to note here is that it does not stay in that Kirkwood gap for long.
More recent numerical simulations have shown the behavior of asteroids in Kirkwood gaps to be chaotic. And they represent the most likely origin for the rogue asteroids that collide with Earth every few eons and cause mass extinctions.