I'll try to explain the best I can. In classical conditioning, you are training the organism to show a fixed response for a stimulus that you trained it, rather than the normal stimulus. Ex: In Pavlov's dogs, dogs salivate when they see t-bone steak (so do I lol). Now, the salivate is the fixed response to seeing steak. Now, when presenting the steak, the scientist would ring a bell (new stimulus you designed). After a while, the dog will salivate to the bell alone.
Now for Operants. Here you also have a fixed response, but you can train the animal to do it more by coupling it with a reward, or train the animal to stop by punishing. Ex: In a cage, there is a tree post. A woodpecker is placed in the cage, and naturally pecks the post. Now, if you want to train the woodpecker to stop exhibiting the pecking behavior, you could place an electrode in the post, so whenever it gets pecked the animal is shocked........after a while, the woodpecker no longer pecks on that post. Now you can also enhance the pecking behavior like so: Place two posts in the cage, of two different colors (we'll say blue and white) Set the woodpecker loose. However, everytime it pecks the blue post, reward the woodpecker..........soon after a while it will only peck the blue post. This is operant.
I hope those are good explanations. Anyone correct me or add. Hope this helps.