Resonance, according to wikipedia is "tendency of a system to oscillate at maximum amplitude at certain frequencies." It was discovered by Galileo by using pendulums.
"One familiar example is a playground swing, which acts as a pendulum. Pushing a person in a swing in time with the natural interval of the swing (its resonance frequency) will make the swing go higher and higher (maximum amplitude), while attempts to push the swing at a faster or slower tempo will result in smaller arcs. This is because the energy the swing absorbs is maximized when the pushes are 'in phase' with the swing's oscillations, while some of the swing's energy is actually extracted by the opposing force of the pushes when they are not."
Here are some more examples of resonance...
-the shattering of a crystal wineglass when exposed to a musical tone of the right pitch (its resonance frequency).
-why your car make shake at a certain speed, but not at others
-when you are trying to break a small tree there is a certain rhythm that is needed to break it.
-In 1981 resonance caused by people dancing on walkway at the opening of a hotel in Kansas City caused it to collapse.
-Some people think that the biblical story of the walls of jericho crumbling may have been caused by resonance from the blowing of the horns that preceded the walls falling.
-Napoleon knew to have soldiers not march in unison over bridges for fear of collapse.
-The Tacoma Narrows Bridge collapsed when the wind was blowing at a certain frequency that matched the natural frequency of the materials of the bridge.