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Nuclei are composed of protons and neutrons, and when lighter nuclei combine to form heavier ones that process is known as nuclear fusion. Binding energy of the protons and neutrons (nucleons) in a nucleus increases with increasing size up to the element iron, after which the binding energy per nucleon starts decreasing again. That means that combining two elements lighter than iron through a nuclear reaction will usually release energy.
The fusion reactions that power the sun are effectively combining four protons (hydrogen nuclei) to make one helium nucleus - the reaction also releases two positrons and two neutrinos in the process, as well as a lot of energy. Practical fusion reactors on Earth are being pursued using several different technological approaches; most make use of the heavier isotopes of hydrogen (deuterium and tritium) to allow fusion reactions to be performed at reasonably achievable temperatures. Artificially controlled fusion has certainly been achieved experimentally in many different situations, but we still seem to be at least decades away from the first practical power reactors.