In fusion, two nuclei have to get extremely close to one another - this means overcoming the large energy barrier (Coulomb Barrier) created by the electrostatic repulsion between the two nucleon's protons. Quantum tunneling is critical for nuclear fusion to occur, because the nuclei involved do not classically have enough energy to overcome the Coulomb barrier and fuse from kinetic energy alone. If they have close to enough energy, they can tunnel through the remaining barrier.
Barrier Transparency, is often approximated by the http://en.wikipedia.org/wiki/Gamow_factor" [Broken], which is the probability for two nuclei to overcome the Coulomb barrier and undergo fusion.