What do you understand by the law of conservation of energy? Discuss how it works in case of simple pendulum

Energy can neither be created nor destroyed it can only be transformed from one form of energy to another. 

Consider a simple pendulum suspended from a rigid support.

Let A be the resting position of the bob when it has zero potential energy. When the bob of the pendulum is displaced to B from its resting position A, the bob gets raised by a vertical height h, so its potential energy increases by mgh if m is the mass of the bob.

On releasing the bob at B, it moves back to A. Its vertical height decreases from h to zero, so its potential energy decreases from mgh to zero, and it gets converted into kinetic energy, i.e. ½ mv² = mgh.
At the point B, the bob acquires a velocity , so it moves towards C. At the point C, when the bob reaches to a vertical height h above the point A, it again acquires potential energy mgh, and its kinetic energy becomes zero. So the bob momentarily comes to rest at the point C. However, due to the force of gravity, the bob moves back from C to A.
Thus during the entire process the total energy of the simple pendulum (sum of kinetic energy and potential energy) remains conserved.