A fission reaction is one in which a heavier atom is split to form a lighter one. The decrease in mass is converted to energy as given by the formula E = m*c^2, where m is the decrease in mass and c is the velocity of light.
A fission chain reaction occurs when the number of reactions which result from one fission reaction taking place is not less than one. If a reaction results in more than one new reaction taking place the increase in temperature and active particles available further increases the frequency of reactions, which is referred to as a chain reaction.
An example of a this kind of a reaction is the splitting up of Uranium 235 when it absorbs a neutron. The reaction results in the generation of two neutrons in addition to other atoms. The neutrons cause two fission reactions to occur in the next stage. As the number of reactions is effectively becoming double at each stage it results in a chain reaction.