Oscillation is the variation, typically in time, of some measure as seen, for example, in a swinging pendulum.
The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with oscillation.
Oscillations occur not only in physical systems but also in biological systems and in human society.
The simplest mechanical oscillating system is a mass, subject to the force of gravity, attached to a linear spring.
The system is in an equilibrium state when the weight of the mass is balanced by the tension of the spring.
If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium.
However, in moving the mass back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position, establishing a new restoring force, now in the opposite sense and this time due to gravity.
The time taken for an oscillation to occur is often reffered to as being the oscillatory period.