Quantum Tunnelling

Essentially, when nucleons are very close to each other they are repelled by the electrostatic force and attracted bby the strong nuclear force. The strong force is stronger at small seperations, making a potential well that holds the nucleons, but the electrostatic force dies off less quickly than the strong giving this high potential point called the coulomb barrier (in the diagram).

In classical physics any nucleons wanting to fuse would have to have enough energy to get over the coulomb barrier in order to fuse- you can imagine it like pushing it up a hill, needing enough energy to get to the top before it can go over the other side into the valley. The problem with this is, in practice particles would never have enough energy to fuse into nuclei, which is why we need quantum mechanics to explain the process.

Basically, quantum tunneling means the nucleons can 'tunnel' through the coulomb barrier even when they don't strictly have enough energy to fuse. It's tied in with the uncertanity principle because the energies of the particles have an uncertainity which allows them to tunnel under certain conditions.