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.
Tunneling first solved a real puzzle in nuclear physics. In 1928, physicist George Gamow used it to explain alpha decay, the process by which certain unstable nuclei eject a small cluster of particles, since classical physics could not account for how those particles escaped a nucleus that should have been holding them in far too tightly. Decades later, the same effect became the working principle of the scanning tunneling microscope, invented in 1981, which drags an extremely fine needle just above a surface and measures the tiny tunneling current that flows between the tip and individual atoms, letting scientists image and even move single atoms one at a time, a feat that earned its inventors the 1986 Nobel Prize in Physics.
Tunneling also plays a quiet role in radioactive dating. Many of the isotopes used to date rocks and fossils decay via alpha emission, the same tunneling process Gamow first explained, and the fixed, statistically predictable rate at which that tunneling happens is exactly what gives radiometric dating its reliability over timescales of millions or billions of years.