Off the top of my head from nuclear power school (only 18 years ago for me)…
Basically, prompt criticality in a pressurized water reactor is avoided by use of the moderator. The pressurized water reactors that I am familiar with use enriched uranium fuel and ordinary water for the moderator.
Indeed, the whole point in having a controlled nuclear reaction is to avoid prompt criticality. This accomplished by the use of Uranium-235, which does not readily fission using fast neutrons (the neutrons produced in a fission event). Uranium-235 has a relatively low nuclear cross-section for fast neutrons. (The units for nuclear cross-section were amusingly named barns, as in the chance of hitting the broad side of a barn.) After neutrons collide with similarly sized subatomic particles (such as the hydrogen in water), they slow down, producing so-called thermal neutrons.
Uranium-235 has a much higher nuclear cross section for thermal neutrons. In other words, a thermal neutron is far more likely to cause a fission than a fast neutron for U-235.
What you want to do is to set up the reactor so that criticality can just exactly be reached primarily with thermal neutrons. This helps create what is referred to a negative temperature coefficient of reactivity. As the moderator (water) heats up, it becomes less dense (though it is still very hot, it is kept liquid by the high pressure). This results in fewer thermal neutrons being produced, so the reaction rate decreases, and the temperature decreases. This results in a feedback loop that controls the reaction.
If an accident were to occur, and the moderator all leaked or flashed to steam, the reaction therefore automatically shuts down, because no more thermal neutrons are being produced.
An out-of-control reaction results if you were to increase the reactivity of the system (say by continuously withdrawing the rods past criticality) until there are enough fast neutrons present to maintain the reaction. This is referred to as prompt critical, and the reaction will go out of control. This is desired in an atomic bomb, but not a power reactor. Because of the geometry of a power reactor, though, it is not possible to get it to actually blow up like a bomb, but it will result in a big mess.
I may have missed a couple of details, but I believe that I have the basics correct here.