The fission events produce a high proportion of fast neutrons. The fission cross-section, ie chance of inducing a fission event when struck by a neutron, depends on the speed of the incoming neutron, and is smaller for the faster neutrons than for slower neutrons.

Thus by slowing the fast neutrons down there are more neutrons with a greater chance of causing a fission event, hence stronger chain reaction.

More neutrons will be able to interact with the fissile nuclei rather than just fly out of the reactor, so you get more fission events.