Classical conditioning is a psychological process that can condition any subject to do pretty much anything within normal boundaries (no, you can't teach your math professor to jump into the gorge in Cornell University).

The man who came up with the whole idea was Ivan Pavlov. He was actually a famous Russian psysiologist, who wrote a famous paper on the digestive systems of dogs. That was probably what led him to his place in modern psychology now.

He noticed how when his assistants brought the dogs food to prepare them for his studies, they would salivate. After a while, every time the dogs saw the assistant, it would drool even if there was no food. Interesting.

Consider a hungry dog who sees a bowl of food. Something like this might happen:

Food ---> Salivation

The dog is hungry, the dog sees the food, the dog salivates. This is a natural sequence of events, an unconscious, uncontrolled, and unlearned relationship. See the food, salivate.

Now, when Pavlov presents the food to the hungry dog (and before the dog salivates), we ring a bell. Thus,

Bell with Food ---> Salivation

Pavlov repeated this action (food and bell given simultaneously) at several meals. Every time the dog sees the food, the dog also hears the bell.

Pavlov continued to do another experiment. He rang the bell, but we don't show any food. What does the dog do? Obviously,

Bell ---> Salivate

The bell elicits the same response the sight of the food gets. Over repeated trials, the dog has learned to associate the bell with the food and now the bell has the power to produce the same response as the food.

This is the essence of classical conditioning. It really is that simple. You start with two things that are already connected with each other (food and salivation). Then you add a third stimulus (bell) for several trials. Eventually, this third thing may become so strongly associated that it has the power to produce the old behavior.