Nuclear fusion
Hydrogen fusion is an instance of nuclear fusion, where the nuclei of multiple Hydrogen atoms combine to form the nucleus of a Helium atom.
Hydrogen nuclei do fuse naturally, under conditions of very intense pressure and heat, such as in the core of a star like Sol, Earth's sun.
Heavier elements will also fuse, under even more intense pressure and heat. But Hydrogen fusion releases much more energy than the energy released by Helium, Carbon, and other relatively light elements. This is why stars rely on Hydrogen fusion for most of their luminous period.
Hydrogen bombs also rely on Hydrogen fusion, for their destructive power. At the heart of every Hydrogen bomb there is a fission bomb, and the explosion of that fission bomb generates the intense pressure and heat to trigger the fusion of Deuterium, the isotope of Hydrogen where the nuclei has both a proton and a neutron.