All matter is made up of atoms. The central body of an atom is called a nucleus. The nucleus consists of protons (positively charged particles) and neutrons (particles with no electrical charge). Electrons (negatively charged particles) are located outside the atom’s nucleus.
In some types of atoms (like uranium), the nucleus is unstable and capable of breaking up, thereby releasing that atom’s neutrons. When those "on-the-loose" neutrons hit other atoms (more uranium atoms, for example), they ALSO split. The splitting of those atoms is called "fission." Fission (in a chain reaction) releases more neutrons plus heat.
(The discovery of fission by German scientists, in 1938, led Einstein and his colleagues to worry that Germany could create a new type of bomb. Concerned, Einstein sent a letter to President Roosevelt. Although FDR created a commission as a result of the letter, not much was initially done about it. It ultimately led, however, to the "Manhattan Project" and the Hiroshima and Nagasaki bombs.)
Splitting atoms - or nuclear fission - produces energy (in the form of heat) called nuclear energy. The key to controlling the splitting of atoms, thereby managing the power of nuclear energy, lies in knowing how to stop the chain reaction. Enrico Fermi, at the University of Chicago, discovered how to do that. His nuclear reactor was the first in the world.
Today, power plants in various countries use nuclear reactors (instead of burning coal) to create electricity. The same concept applies to nuclear-powered submarines where the energy produced from nuclear reactions (not fossil fuel) powers the ship. Always at issue, among other things, is the safe disposal of nuclear waste.
On 29 August 1949, the Soviet Union detonated its first nuclear (atomic) bomb. The Cold War, with its threats of mass destruction and political domination, had begun.
With the arrival of K-19, in 1961, both the U.S. and the Soviet Union possessed nuclear-powered submarines equipped with nuclear-tipped ballistic missiles. The arms race, it is often said, can be directly traced to those submarines.