Nuclear fission is vastly more energetic than the chemical reaction of an equivalent mass could be. The implosion-style Fat Man bomb that was dropped over Nagasaki, Japan, for example, contained 14 pounds of plutonium. A conventional chemical explosive would have required more than 20,000 tons of TNT to deliver the same yield.
Chemical reactions deal with the formation and decay of the bonds between atoms and molecules. Such reactions can be simple and well understood or complex and unpredictable. Chemical reactions are usually sensitive to their environment in that temperature, air pressure and the presence or absence of other chemicals can radically alter the outcome of the reaction.
Nuclear fission is the process of splitting the nucleus of a heavy element, usually a metal such as uranium or plutonium, to produce lighter decay elements. The process is simpler than most chemical reactions, and it can be understood in terms of fundamental physics. The chemical environment in which fission takes place is largely immaterial, though the environment inside a reactor vessel is carefully controlled, as the reaction takes place entirely within the atoms' electron shell.
Atomic fission is almost always undertaken in an effort to generate energy. While combustion reactions liberate the chemical compounds' stored energy, fission reactions for the equivalent mass are about 2 million times more energetic.