A Tesla coil is a resonant transformer: its secondary winding builds up an intensely high-voltage oscillating electric field around the toroid. When the field gets strong enough, it ionizes and breaks down the surrounding air (dielectric breakdown), discharging as branching, jittering lightning-like arcs that jump to nearby grounded rods. The arcs continually re-strike and flicker because the coil re-charges and the air path re-ionizes many times per second.