Galileo noted that the swings of a pendulum increasingly grow with repeated timed applications of a small force. This phenomenon is called resonance and it occurs when the frequency of an applied force matches the natural frequency of a system. Large-amplitude oscillations are the results of resonance.

Let's take a spring system for example.
The spring moves up and down when an initial force is given to stretch or compress the spring. This motion of moving up and down is called a harmonic motion. ( Motion in which the restoring force has the mathematical form given by Can also be thought of as a motion which has a sinusoidal, or like a cosine, sine curve, shape with an amplitude when graphed of its position as a function of time. )

Suppose that this force is applied at all times, not just for a brief initial moment. This additional force is known as the driving force . When the driving force has the same frequency as the spring system and always points in the direction of the objects's velocity, a great increase in the amplitude of the vibration occurs.
This is how resonance is made.

The natural frequency of a spring system is shown below.

Resonance explains why a swaybridge (Like the Tacoma's narrows bridge) collapsed in a mild wind and how a wineglass can be shattered to pieces by a human voice.