Negative reinforcement is a term described by B.F. Skinner in his theory of operant conditioning. He explains it as a response or behavior that is strengthened by stopping, removing, or avoiding a negative outcome or aversive stimulus.
Think of this reinforcement as something being subtracted from the situation.
Negative reinforcement uses two different types of behaviors: escape and avoidance.
In escape behavior the occurrence of the behavior terminates the aversive stimulus. Where in avoidance behavior, the occurrence of the behavior prevents the presentation of an aversive stimulus.
Both escape and avoidance are types of negative reinforcement, both result in an increase of the behavior that terminated or avoided the aversive stimulus. Both create emotional responses that say, phew, thank god that is over.
This reinforcement is seen most effective when reinforcers are presented immediately following a behavior. When a long period elapses between the behavior and the reinforcer, the response is likely to be weaker.
For example, with animals the beep on the shock collar before the shock. The dog is now aware of what that noise means due to its conditioning history that the beep predicts pain if the current behavior continues.
Example of Negative reinforcement in the show Big Bang Theory: