In a nuclear reactor, a moderator is any substance that slows a neutron down to thermal energy, thereby increasing the probability that it will cause another fission. Neutrons that are direct products of prompt or delayed fission are moving too fast to be absorbed by 235U, and therefore need to be slowed down. Several factors contribute to a good moderator and to the ideal amount of moderation in a reactor core.
First, a moderator needs to be able to slow down neutrons, as this is its primary function. Neutrons are slowed when they lose kinetic energy in a collision. With a particle as small as a neutron, the collision will be almost completely elastic, meaning that the kinetic energy will have to be transferred to whatever the neutron collides with if it is to slow down. The best moderators, then, have a mass close to that of a neutron. This is why small molecules like water are often chosen.
Almost as important, though, is the resistance a moderator needs to absorbing another neutron. The ability to absorb a neutron is expressed as a probability given an area unit called a "barn." (Seriously, as in "You couldn't hit the broad side of a barn.") This is why heavy water, or deuterized water, is often used. Water made with one oxygen atom and two deuterium atoms is so resitant to absorbing neutrons that reactors running with heavy water as a moderator can use natural uranium that has not been enriched. The only problem is that it costs as much to make heavy water as it does to enrich uranium.
So aside from water and heavy water, graphite is a popular moderator, because it also works as a reflector to keep neutrons inside the core instead of leaking out to where they are not useful. Another common moderator is zinc hydride, which in some reactors is mixed homogenously with the fuel itself.
Moderation is a very important balance in a reactor. If a reactor has the perfect amount of moderation, it has the highest power efficiency. Too much moderator in respect to fuel creates a situation called overmoderation. The opposite condition is undermoderation. Overmoderation can be dangerous, because this means when a moderator becomes less efficient, which tends to happen when it gets warmer, the reactor actually increases in power. No reactor in the United States is overmoderated; they are all undermoderated. This means that as power increases, the core temperature increases and it becomes more difficult to increase in power. Smart design of nuclear reactors is necessary to keeping them a safe source of energy.