According to Quantum Mechanics, a particle has a definite probability of being anywhere in the entire universe. Although any real distance from the particle’s expected classical path is infinitesimally small, since Quantum Mechanics is a statistical theory those small probabilities must be counted!
Quantum Tunneling is a fascinating effect that arises out of these small probabilities. This effect allows particles to occasionally pass right through obstacles that it would not normally have the proper energy to overcome, or an electron to escape the ‘pull’ of the nucleus without having enough kinetic energy to do so.
Although it’s fairly obvious that atoms are not just randomly going through every barrier, but this is because the probability of that happening is astronomically small because the barriers in our everyday world are rather thick. If made thin enough (approximately 1-3 nm,) the chance that a particle will spontaneously pass through becomes noticeable. A particle can effectively ‘borrow’ energy from the system that it’s acting in, pass through a barrier, and then spontaneously lose it. Mathematically, this can be explained using Heisenberg’s uncertainty principle, which limits the amount of information that can be known about any particle.
Quantum Tunneling is responsible for many interesting happenings throughout our universe, including enzymes in our own bodies. However, we can thank Quantum Tunneling for the sun’s heat. The sun is massive - very massive. However, in order to produce the temperatures necessary to activate nuclear fusion, the sun should be mathematically be much more massive! Due to Quantum Tunneling, there is a small chance that a Hydrogen atom will spontaneously undergo nuclear fusion without the proper temperature. However, since the sun has a tremendous amount of Hydrogen atoms in it, this small chance is converting about four million metric tonnes of Hydrogen each second!
So basically you would not exist here today because stars would not behave the way they do if it wasn’t for quantum mechanics!