In a reactor, nuclear fission is initiated by bombarding fissile nuclei with neutrons. In the subsequent fission of a nucleus there is always a release of neutrons which can in turn cause the fission of other nuclei releasing more neutrons and so on. This cascading fission forms what is called a chain reaction.
In a reactor, this reaction must be kept under control. A classic reactor runs in the critical regime: the fuels used (some are fissile while others absorb neutrons) are designed so that only one of the neutrons released during each fission causes a new fission. In a sub-critical reactor the fuel is chosen so that less than one neutron per fission causes a new fission. Such a reactor cannot therefore sustain a chain reaction by itself. It must be supplied with neutrons from an external source minimising the risk of any runaway accidents.