Differences between 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.