quantum tunneling
Roll a ball at a hill and, if it is moving too slowly, it rolls partway up and comes back — it cannot reach the other side. Quantum tunneling is the strange fact that very tiny things, like atomic nuclei, sometimes appear on the far side of such a hill even when they did not have the energy to climb over it. It is as if the ball, now and then, simply turns up beyond the hill without going over the top. This is not a metaphor or a trick; it is a real, measured consequence of quantum mechanics.
Quantum theory says a particle does not have one exact location but is described by a wave of probability that is smeared out in space. When that wave meets a barrier — like the Coulomb wall of electric repulsion between two nuclei — most of it bounces back, but a thin sliver leaks through to the other side. So there is a small but nonzero chance the particle is found beyond the barrier it 'should not' have passed. The thicker and taller the barrier, the more sharply that chance shrinks, but it is never exactly zero.
Tunneling is precisely what lets the Sun shine. At its core temperature, nuclei almost never have enough speed to climb over their mutual Coulomb barrier the classical way; without tunneling, fusion would essentially stop and the Sun could not exist as it does. Because tunneling is rare for any single pair of nuclei, fusion proceeds extremely slowly — which is exactly why the Sun's hydrogen lasts about ten billion years rather than flaring out in an instant. The same effect underlies radioactive decay and is harnessed in some modern electronics.
Run the numbers classically and the Sun's core is far too cool to fuse hydrogen — by the old physics it should be dark. Allow quantum tunneling, and a small fraction of nuclei sneak through the barrier each second, exactly enough to power the Sun. Tunneling is why the sky is bright.
Without quantum tunneling the Sun could not fuse hydrogen and would not shine.
Tunneling makes fusion possible but still rare for any one collision — it does not make fusion easy. That rarity, not abundance, is why the Sun burns slowly and steadily for billions of years instead of detonating.