Moderation is the process of slowing neutrons in a nuclear reactor so that they can easily promote fission of a nucleus. The material that causes this slowing down of the neutrons is known as a moderator.
Neutrons come out of a fission event with energies between 1 and 10 MeV, which is too high to reliably create another fission event. This is because the cross section for neutron capture (the likelihood that an isotope will absorb a neutron, leading to a fission event) is greatest for neutrons that have an energy of only 1 eV, a million times less. Neutrons with energies less than one electron volt are known as thermal neutrons since they have energies similar to what particles have as a result of ordinary room-temperature thermal energy. Because the likelihood of fission is higher with slower neutrons, the neutrons must be slowed to this thermal range before fission is likely to happen.
There is some slowing of the neutrons when they scatter inelastically with the non-fissionable uranium-238, however there must still be a moderator for the nuclear reactor to operate properly. Neutrons collide elastically with the nucleus of the moderating medium, transferring some of its energy to the nucleus. This causes the neutron to slow. Note the simulation above, this shows how certain nuclei in the moderator slow the fast neutrons as they collide.
Neutron moderators are a type of material in a nuclear reactor that work to slow down the fast neutrons produced by fission to make them more effective in the fission chain reaction. A separate moderator material is required because certain materials are better moderators than others. By looking at conservation of energy and momentum it becomes clear that a if a neutron (with mass of only a single atomic mass unit) will not slow down much after a collision with a heavy nucleus, like an atom of uranium fuel (with a mass of 235 atomic mass units). If this neutron collides with a smaller atom - such as hydrogen - it can slow down dramatically. This is one reason why water makes a good moderator. Light water slows down neutrons more quickly, but absorbs more neutrons, while heavy water slows down neutrons more slowly but doesn't absorb as many. This is one of the reasons why a heavy water reactor like a CANDU is so much bigger than a light water reactor, more moderation is needed.