Jacob's ladder, more formally known as a high-voltage travelling arc, is...well...a high-voltage travelling arc. When the voltage difference between two electrodes exceeds the breakdown voltage, a spark forms. In this case, the spark forms between the vertical wires (the electrodes) near the bottom, where they are closest. The spark rapidly changes to an electric arc (a matter of nomenclature at this point, as a spark is generally a very quick and temporary occurrence while an arc is a sustained discharge). The arc heats and ionizes the air in its immediate vicinity. The ionized air maintains the arc, but the heat causes the ionized air to rise, thus the arc rises with the heated and ionized air, becoming less and less stable as it climbs and the separation between the wires increases, until the arc finally breaks. Then it starts again at the base.
