Resonance is a phenomenon for oscillating objects where an external force is being applied to the object, causing forced oscillations.  This is similar to pushing someone on a swing.  The person on the swing can continue swinging by itself, under the influence of gravity, and it does so freely at a normal, natural frequency.  When a second person comes along and begins pushing on the swinging person.  There can be two different frequencies in this system, the natural frequency of the swinging person, f_nat, and the ‘forced’ frequency at which the second person is pushing, f_forced.  The result is the swinging person will now be forced to swing at the forced frequency.  But one other thing about this situation is that the person pushing on the swing will get tired and the swinging person will notice it is not going very high – this is not an efficient use of energy and is not much fun.

However, if the person pushing on the swing such that the he or she matches the natural frequency of the swing, then the pusher will discover he does not get very tired and the person on the swing notices she is going higher and higher.  When the pusher and the swinger are doing so in synch with each other, such that f_nat = f_forced, the system is in resonance.  This is where the efficiency is highest the swing gets to its greatest amplitude.