Like many of Tesla’s inventions, the Tesla coil exploits the principle of resonance which has become such a common trope in contemporary thought as to warrant a brief description here. Not so much a law of nature as a deep habit, resonance pops up across the board, emerging in electrical systems, steam engines, and molecular dynamics, as well as Tuvan overtone chanting and the tuning of TV sets. Everything vibrates, and when the oscillating vibrations of different systems coincide, or resonate, large quantities of energy can be exchanged from one system to the other.
Davis, Erik. TechGnosis: Myth, Magic, and Mysticism in the Age of Information. New York: Harmony Books, 2004. 86-7.