What is resonance?

Resonance is a phenomenon of maximizing the amplitude of a periodic motion, oscillation, or vibration. The best way to understand how it occurs is by considering a swing. If you are sitting on a stationary swing and would like to get it swinging as high as possible, you need to rock yourself forward and backward in a regular, periodic way. Notice, however, that if you do that very slowly - if your forward/backward motion has low frequency - you will not be able to swing very high. If you do it too quickly, it also won't work - the swing will not move. You have to figure out, by trial and error, exactly how often you need to lean forward and then lean back so that the swing will start reaching higher and higher every time it goes up. The frequency you have found equals the "natural" frequency of "you and the swing" system - this would be the frequency of your motion if the swing with you on it was pushed once and then left alone. Similarly, if you are pushing someone else on a swing, you will get the best results - that is, the maximum amplitude - if you push every time the swing is at it highest point. By doing this, you again make sure that your "driving" frequency equals the natural frequency of the "swing and someone else" system.
Resonance can be established in any system, not necessarily mechanical, where the periodic motion, or oscillation, occurs. For example, oscillation of electrical current can be established in a circuit consisting of a capacitor and an inductor. The natural frequency of the circuit would depend on the capacitance and the inductance.This oscillation would die down - decrease in amplitude until there is no current left - due to the resistance in the circuit. However, if the circuit is connected to the external voltage source supplying the voltage with the same frequency as natural, the amplitude of the current will reach its maximum possible value. Also, a radio station broadcasting a signal at the natural frequency of such a circuit will establish in it electrical oscillations with maximum amplitude. These oscillations can then be converted into sound - which is what is done in a radio receiver, and other electronic devices. 
The reference links below describe other examples of resonance, such as the resonance in air columns and strings.
 
http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/reson.html

https://www.physicsclassroom.com/class/sound/Lesson-5/Resonance