So the “Bang” in an atomic bomb comes from the energy produced in nuclear reactions. A small amount of matter is turned into a vast amount of explosive energy. The famous equation by Einstein, E=MC^2 , explains this. It says that Energy and Mass are the same and that a little bit of mass contains a lot of energy. So what mass is inside an atomic bomb? Well different bombs have different elements inside them, but it is usually uranium or plutonium, The US dropped an atomic bomb of both types on Japan (uranium on Hiroshima, plutonium on Nagasaki) at the end of world war II.
There are also atomic bombs that used nuclear fusion (the ones above use nuclear fission) which contain isotopes of hydrogen (deuterium and tritium). These are sometimes known as hydrogen bombs.
During the cold war, the Russians detonated one of the biggest hydrogen bombs ever, the “Tsar Bomba”. Soon after, every one realised that we had enough bombs to wipe out every one on the planet many times over. That is probably when people started thinking about controlling “nuclear proliferation” (letting every one have nuclear bombs)