An ongoing series of fission reactions is called "chain reaction".
A fission is a nuclear reaction in which a nucleus of a heavy element breaks up into several nuclei of lighter elements, releasing energy in the process.
A typical example of a fission reaction is that of a uranium (`U^235` ) nucleus (please see the reference link for a detailed description.) When a nucleus of a uranium atom is hit by a neutron, the neutron and the nucleus may bind together due to the nuclear force. However, the resultant nucleus is not stable and can undergo fission, that is, break apart into smaller nuclei. Neutrons and gamma rays are also produced in this reaction.
Under certain conditions (again, please see the reference link for details), the neutrons released in a fission of one nucleus will move with just the right speed to hit and be bound to other uranium nuclei, which in turn will also become unstable. They will thus break apart as well, producing more neutrons, which will hit more nuclei, and the chain reaction will begin.