Consider a pendulum. It hangs at rest (position I) in a state called equilibrium.

If the pendulum is pulled to the side (position II), it now has a certain amount of potential energy.

When the pendulum is released, its potential energy becomes kinetic energy, and returns it to position I. At that point, however, its momentum continues to move it past equilibrium. As gravity begins to work against the pendulum's momentum, it stops in a new position (III) with kinetic energy equal to position II.

The cycle then repeats, as the potential energy of position III becomes kinetic energy, swinging the pendulum once more past equilibrium and back into position II.