After a set of capacitors is fully charged to a voltage V, one is discharged (usually by the use of a trigatron) on to the opposite side of the circuit. This induces a voltage swing of V (apparent) to the next capacitor/sparkgap combination in line, which then also fires (as 2V is greater than the gap's breakdown voltage). This then induces a voltage swing of 2V(apparent) to the next cap/gap combo, which also fires, adding its V, making it 3V. This continues for as many capacitors as you have.
PULSE has an 8-stage Marx Generator as its power supply. The generator is driven by a high voltage flyback tranformer system. See the schematics below: