An oscillation is the "back-and-forth" variation of a physical quantity (e.g. position, velocity, current) about a central value or between two or more different values.
An object undergoing oscillations is known as an oscillator.
An oscillator undergoes free oscillation if it is allowed to oscillate without being restrained by external forces. Free oscillations are able to continue on indefinitely because there are no forces resisting the oscillations.
An example of an oscillator undergoing free oscillation would be a simple pendulum (assuming no friction). It comprises a mass suspended from a string, swinging back and forth in a vertical plane without air resistance between two points.
These points are equidistant from a central equilibrium line.