Quantum tunnelling is a quantum mechanical process where a particle tunnels through a barrier that it classically (ie, in classical physics) could not pass. As quantum tunnelling lies in the domain of quantum mechanics, it cannot be perceived directly. However, it can be explained basically with a simple analogy of a person throwing a tennis ball at a brick wall.
When the ball is thrown at the wall it bounces off, returning to its point of origin. This, according to classical physics, would happen every time the ball is thrown – the ball is a physical object and lacks the energy to break through the wall to the other side. It is trapped.
But in quantum mechanics, the particle (ie, the ball) could with very small probability tunnel to the other side of the wall. This is because in quantum mechanics matter is treated as having properties of waves and particles, unlike stated in classical physics. This creates a duality where the probability of a particle crossing the barrier is nonzero and therefore, in consequence, actually crosses the barrier.