Whilst I don't want to demean other members of the forum, I think a topic such as quantum tunnelling is beyond most members ability to explain (understand even) - it's best left to the technical articles linked above!
In really simple terms quantum tunneling can be described as an unlikely event with a small positive probability. If you provide enough trials (particles) some of them will make it through an otherwise impassable potential barrier.
It's sorta like prisoners escaping from a supermax like Pelican Bay.