If nuclei come close enough together, they can interact with one another through the strong nuclear force. As in chemical reactions, nuclear reactions can either be exothermic (releasing energy) or endothermic (requiring energy). The two major classes of nuclear reactions are fusion and fission.
Fusion
Fusion is a nuclear process in which two light nuclei combine to form a single heavier nucleus. The fusion process has real world applications, for example the reaction between two different hydrogen isotopes forms an isotope of helium. This process is important in thermonuclear weapons and in nuclear reactors.
Fusion reactions release huge amounts of energy. When two light nuclei fuse, the total mass of the product nuclei is less than the total mass of the initial. This "missing mass" is conserved through the release of energy during the reaction. The process of fusion gives off a lot of energy which is why this process is able to power stars.
Even though fusion is an energetically favorable reaction for light nuclei, it does not occur under standard conditions on Earth because of the large energy investment needed to kickstart a reaction. Nuclei are positively charged, so when two nuclei approach each other there is a large electrostatic repulsion. Added energy is needed to overcome the repulsion and squeeze them very close to one another in order to allow the nuclei to fuse.
Scientists on Earth have produced multiple fusion reactions throughout the last seventy years. At first, we started with small scale studies in which only a few fusion reactions actually occurred. Eventually these experiments lead to the development of thermonuclear fusion weapons or hydrogen bombs. Outside of weaponry, scientists have hope to use fusion reactions in generating clean and inexpensive power.
Fission
At face value, fission is the reverse of fusion. Fission is a nuclear process in which a heavy nucleus splits into two smaller nuclei. This split occurs because of electrostatic repulsion found between the large amount of protons in a heavy nucleus. Two smaller nuclei have less internal electrostatic repulsion than one heavy nucleus. To achieve fission, a large nucleus must overcome the strong nuclear force that holds it together. The nucleus plays a sort of "tug-of-war" between the strong attractive nuclear force and the repulsive electrostatic force. In fission reactions, electrostatic repulsion wins and the nucleus breaks apart.
Fission reactions can produce any combination of lighter nuclei so long as the number of the protons and neutrons sum up to be the same across the initial nucleus and the products. Even though the number of protons and neutrons need to sum up, fission reactions still release a great amount of energy just like fusion. The fissioning mass will always have a larger mass than the summed masses of the lighter product nuclei, but because mass is a form of energy it is conserved when the fission reaction releases kinetic energy.
Heavy nuclei are often semi stable and when given a kick start of energy, generally from a collision with a free neutron, the nucleus will undergo fission to try and reach a more stable state. This stable state has energy spread out across two smaller daughter nuclei. There are often product neutrons left over in fission reactions and these free neutrons can kick start fission in other heavy nuclei often starting a chain reaction. Nuclear power plants use these a controlled version of these fission chain reactions to generate energy.
A fission process of 235U was used to create the first nuclear bomb, however there are multiple fission decay options for each heavy element that can lead to a different number of daughter isotope products.