Quantum tunneling is what happens when a particle gets through an energy barrier that, by classical physics, it should not be able to cross at all. Because a particle’s position is described by a wave function rather than a single fixed point, there is a small but real chance it appears on the other side of the barrier instead of bouncing off it.
The thinner and lower the barrier, the higher the odds of tunneling through. This is not magic, it follows directly from the mathematics of quantum mechanics, and it has been measured and used in real devices for decades.
Tunneling is why the sun can shine at all, since it lets protons overcome their mutual repulsion to fuse together at lower temperatures than classical physics would allow. It is also the working principle behind scanning tunneling microscopes and flash memory chips.