Nuclear fusion happens when two nuclei (center of an atom) are forced to combine with each other. Since nuclei try to prevent themselves from combining together, fusion only happens under extreme conditions or environments, like the inside of a star! This joining results in a heavier element being formed, and excess energy being released.
Imagine two of the best football players from two opposing teams. If, for some reason, they were forced to join one team together, they may not like it, but a stronger, more powerful team would likely result.