SCIENCE. Psychology. The process by which a response normally elicited by one stimulus (the UCS) comes to be controlled by another stimulus (the CS as well).
Adapted from Psychology: The Science of Behaviour Neil R. Carlson et al

If you didn't get that, classical conditioning is basically a method by which a person or persons is conditioned to react to a specific stimulus that does not naturally cause the reaction. Classical conditioning is not a bad thing. It's something we experience every day in our lives.

For instance, a child can watch a balloon expand (conditional stimulus), and exhibit a startle reaction (response) when the balloon explodes (the unconditional response. If this happens long enough a conditioned response would develop, then the child exhibits the startle reaction, which is now the conditional response, in response to the balloon being expanded.

Obviously someone cannot simply be conditioned by linking the specific stimulus with the response once. Factors such as strength and perceived importance of the stimulus and response, the number of repetitions that have to take place, and the time between the stimulus and the response also play a role.

Classical Conditioning was discovered by Ivan Pavlov in 1904 with his study on dogs (see for the original experiment). Its interesting to note that Pavlov's work was not intentionally a study into animal behaviour, but on the digestive system). Subsequently classical conditioning is also known as Pavlovian conditioning. The concept of using classical conditioning to control the masses, as exhibited in anti-government/anti-communist books such as Brave New World, where citizens are conditioned to enjoy working and fear the outdoors.

See also weird experiences with self classical conditioning.