A behavior chain is when more than one behavior is performed in response to a stimulus. For example, telling a dog to go to his bed and then telling him to lie down. After enough repetitions, when the dog is told to go to his bed, he will automatically lie down without being told.
Chaining is the deliberate creation of a behavior chain. Back chaining is a kind of chaining where the final behavior in a chain is taught first and given a very strong reinforcement history, so that the dog develops a CER+ to performing it. Each behavior is reinforced by the opportunity to perform the next behavior in the chain.