The Tesla Coil is an air-core transformer with primary and secondary coils tuned to resonate. The primary and secondary function as a step-up transformer which converts relatively low-voltage high current to high-voltage low current at high frequencies.
The Tesla Coil demonstrates the fundamental principles of high frequency electrical phenomena. It illustrates the principles of ionization of gases and behavior of insulators and conductors when in contact with high frequency electrical fields.
Its inventor, Nikola Tesla, conceived it to be a means to transmit electrical power without wires. An antenna would pull the transmitted electrical energy into the electrical system. You can also consider it a simple radio transmitter, operating within a broad range of high frequencies, which transmits power rather than information.