A Neutral Stimulus is a stimulus that produces no response other than catching your attention. For example, let's say you have to bring your child to the pediatrician for a shot. Prior to the shot, the pediatrician presses a buzzer to call her assistant to come in and help her administer the vaccine. In this case, the sound of the buzzer is the neutral stimulus because it doesn't produce any response from the child, but the child does notice it.
Each time your child goes to the pediatrician to get a shot, the doctor presses the buzzer before the shot. Now, every time your child hears the buzzer, she cries.
The first time she rang the buzzer to call the assistant, your child had no relevant response. The assistant came in and the pediatrician proceeded to give the shot, which caused your child to cry. After several visits where the doctor would always buzz to call her assistant and then administers the shot, your child began to associate the ringing of the buzzer with the shot. Now, as soon as the doctor rings the buzzer, your toddler starts to cry. The previously neutral stimulus of the buzzer has become what is called a conditioned stimulus, triggering a conditioned response (crying).