Does nuclear fussion occur naturally?
It occurs naturally but not easily since it requires immense pressures and temperatures to proceed.
Atoms and nuclei experience strong electrostatic repulsion forces (between electrons and protons respectively) which increase exponentially as they get closer to one another (the force obeys the ubiquitous "inverse square law"). Therefore, in order to bring nuclei together so that fusion may take place, these strong repulsive forces must be overcome. This can be done through pressure, temperature or, for instance, by accelerating the particles to high speeds and then making them collide (in a particle accelerator).
Nuclear fusion is the process by which lighter atomic nuclei are fused into heaver atomic nuclei. The process is also known as nucleosynthesis.
The first naturally occurring fusion reactions happened soon after the Bi Bang in what is known as Big Bang Nucleosynthesis. The early Universe consisted of Hydrogen. There came a time when the conditions were right for the fusion of Hydrogen into Deuterium, Helium 3 and Helium 4. Small amounts of Lithium and Beryllium were also produced.
The main natural fusion reactors are stars. Stars are formed from clouds of dust and gas which collapse under gravity. As the clouds collapse the pressures and temperatures increase to the point where the strong nuclear force can overcome the electrostatic repulsion of positively charged protons to start and maintain fusion reactions.
Fusion reactors have huge potential as they can produce copious amounts of clean energy. The problem is that maintaining the high temperatures and pressures required for a sustained fusion reaction is proving difficult to achieve.