You've just taken your allowance from your mom, a whole ten bucks. You got very excited and decided to buy a Ferrari! Of course all your friends loved this story, and got a good laugh at you.Not quite. According to quantum mechanics, you can very well get

yourself a nice looking slick Ferrari (worth 120 000) just for your 10 bucks. I'm sure you would like to know how. O.K., I'll do you this favor, but promise to take me on a ride with your new Ferrari.

As you might recall, in quantum mechanics the position of a particle for example is described by a wave function which tells us that this particle is a superposition of several possible positions. So, your allowance can be nothing but a superposition of several "allowances". Although the "average" allowance which your mother gave you might not be enough to buy a Ferrari, "one" of the allowances which constitutes your average" allowance might be just enough to get you your dream red Ferrari.
That's what we call "tunneling effect".

Look at this ball below. If its energy is not enough, it can never escape from the bowl. But that's in classical mechanics. If we use a quantum ball, there are situations in which the average energy is too small for the ball to escape (your mom's allowance), but yet there is some cases where the ball can assume enough energy to escape on the quantum level (enough money to buy the Ferrari). Thus it can happen that a quantum ball starts well inside the bowl with an average energy too small for classical escape, yet nevertheless the ball escapes. This process is called tunneling, because it is a way to get out of a barrier without going over the barrier.

Practical applications

"The scanning tunneling microscope" can easily locate individual atoms.
In this device a thin needle moves across the surface of a sample. Electrons can tunnel from the needle to the sample, but only if the two are very close. In this way, a very precise picture of the sample's surface can be built up.

Perhaps the one application of the tunneling phenomena which is fundamental to our own life is the generation of sun shine! The sun produces light energy through a series of nuclear reactions. The first step in this series is that two protons come very close to each other and react to form a proton and neutron bound together, plus a positron plus some other smaller particles ( antielectron+neutrino). The important thing is that the two protons have to come close together. But the two protons have the same electric charge, so they repel each other strongly. Calculations based on classical mechanics predict that this reaction would happen so slowly that almost no light would come from the sun. A correct calculation based on quantum mechanics shows that one proton tunnels through the barrier of repulsion separating the two, and allows the reaction to proceed.

Quantum mechanics applies to the domain of the very small, but sometimes small things have big consequences. Sunshine itself is generated through the workings of quantum mechanics.