A thing that is moving back and forth or to and fro is said to be vibrating. Another word for vibration is oscillation. A special way of vibrating or oscillating is called "simple harmonic motion". When measuring motion, it is normal to make a graph with time on one axis and distance on the other. Sometimes, when something moves its distance from a fixed point looks like a sine wave if it is written down in that kind of graph. In mathematics and physics this is called simple harmonic motion. This sort of movement will happen whenever the force towards the fixed point is proportional to the distance from the point (the force goes down as much as the distance goes up) and always acts towards that point. Some examples are a weight on a spring and a simple pendulum (for small oscillations). These are not perfect examples, but they are close to having simple harmonic motion. 