When a ball rolls down from the edge of a bowl, it barely reaches the opposite edge and comes back oscillating until friction slows it down to a stop in the bottom of the bowl.
If you reduce your ball to an electron and your bowl to a potential well (see this as a tiny bowl, working with electric fields rather than gravity), not only there is no friction to speak of, but if there is an other "bowl/well" nearby, the electron may jump out of the first bowl and appear in the next without ever reaching the edge of either bowl. This is tunneling. The way it works is by probability. The probability of tunneling is never zero, but can be increased by bringing the bowls/wells closer to each other, or by lowering the edges (even though they can be maintained above what would be required classically for the ball/electron to transfer). Funky huh? That's what's fun about quantum mechanics.