Particle or Wave?
How does light travel? Everyone could have different ideas about it, but according to Maxwell’s Equations it actually depends. This might sound awkward but it is. Before the equations of Maxwell, the photon (light packet) was thought to travel as particle. You might have heard about the double slit experiment. If you did not, it basically concludes that photon does not exactly travel as particle, additionally they travel as waves too. Actually they mostly travel as waves in vacuum also known as space.

Source: https://www.linkedin.com/pulse/exploring-quantum-insights-metrics-monitoring-study-thomas-alagesan/
Wave Nature of Quantum Particles
After talking about the discovery of wave nature of quantum particles, we have to explain Schrödinger’s equation. It basically states that quantum particles (electron, photon etc.) can be at very distinct locations in the same time. You might think that it is illogical, furthermore impossible, but it is possible and explained. This is what Schrödinger’s equation interprets to.
According to Wave Function, the travel of electrons is not definite and it is dependent on probability distribution. The distribution gives the chance of electron being there. Additionally the origin of this depends on Heisenberg’s Uncertainty principle, so for curious they can check it out for more info.

Source: https://physicsmax.com/electron-probability-distributions-5142

Source: https://www.science.org/doi/10.1126/sciadv.adg8516
Getting Through Objects
We have all seen in movies that the character pass through some objects such as walls. After explaining the wave function and electron distribution, we can say that electrons are based on probability. So let’s think that we have a barrier that is slim enough to get pass through it. Keep in mind that the slimmer the barrier gets, the more probable the action is. If we send an electron to barrier, it would come back as it is a wave. Even though the wave comes back, there is a very small chance of going through it. The part that is gone through is tunneled. Keep in mind that the tunneling has a very small percentage, but it is still possible.

Source: https://phys.libretexts.org
Why Electron Has This Probability?
Physicists have a general method for solving the problems. Putting under light. This might sound crazy, but since the discovery of photon being an electromagnetic force carrier, the impact of light in the area of physics is indispensable. Almost every area of physics uses and investigates the photon, yet there is a fundamental area of it which is Optics. Optics does not necessarily interest with light being electromagnetic, but it is being observed before the discovery of photon. As you may know from school, the light refracts when it changes environment. The scattering of light when it is reflected from a lens, it lefts a small scattering called an evanescent wave. The evanescent wave is based of probabilities since it is a wave. So, we have a probability of going out of lens. The same property goes for the tunneling. This is the reason why electrons can tunnel.

Source: medium.com
Bibliography
- medium.com/@prmj2187/quantum-tunneling-when-particles-defy-classical-constraints-b001691c3769b
- linkedin.com/pulse/exploring-quantum-insights-metrics-monitoring-study-thomas-alagesan/
- physicsmax.com/electron-probability-distributions-5142
- science.org/doi/10.1126/sciadv.adg8516
- phys.libretexts.org
- en.wikipedia.org/wiki/Quantum_tunnelling
- youtube.com/watch?v=WPZLRtyvEqo
- phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.07%3A_Quantum_Tunneling_of_Particles_through_Potential_Barriers
- byjus.com/physics/quantum-tunnelling/