What is the Difference of Operant Conditioning and Classical Conditioning

Classical conditioning is where one thing is "programmed" into the brain, and is associated with another. See Pavlov's dog experiment for a nice example. This can be anything relating to anything, and is thought to have a lot to do with irrational phobias.

Operant conditioning, or operant learning, is where something is learned by the consequences, and if more of a trial-and-error type of learning. For example, a child does something bad, and is scolded by it's mother. the child learns that doing that behaviour will result in a scolding. Operant conditioning research has shown that rewards are better responded to than punishments.