A Tesla Coil is a loosely coupled resonant transformer, which Tesla used to create high frequency, high voltage currents, and later to transmit energy through the earth. Modern day “Tesla Coilers” use this type of circuit to create big sparks, but Tesla himself on the other hand aimed to suppress spark losses from the top terminal by maximizing the surface area, as can be seen in the following patent drawing:
Tesla powered his Tesla Coils by discharging capacitors through a spark gap, which in turn set up a high-frequency oscillating current in a primary of a few turns. This also induced an oscillating current in a secondary of many turns, due to resonant inductive coupling, which greatly increased the voltage. Modern Tesla Coils are now often powered by a function generator + amplifier combination.