The spring is held firmly at the other end. Let the spring along with the steel ball be kept steady at an equilibrium position. Now pull the ball down, displace it by a distance x and release it. You will notice that the steel ball is performing an up and down motion. The word harmonic implies that the motion is periodic in nature.
Periodicity shows that the ball returns to the same position after an interval of a definite time.
If we analyse the motion carefully, we will see that when the steel ball is pulled down by distance x, the spring is stretched by a distance x. Because the spring is elastic in nature, it will try to restore its original shape or position. Let F be the restoring force. It is easy to understand that the restoring force is proportional to the displacement x and acts in the opposite direction. This means that larger is the displacement, larger will be the restoring force, which will try and bring back the steel ball to its equilibrium position.