This is a Marx generator, a circuit that uses spark gaps to build a high-voltage pulse. A 5kV input voltage charges the capacitors until the first spark gap reaches its breakdown voltage and fires. This causes a large voltage to be applied to the second spark gap, causing it to fire as well. All the spark gaps fire in turn, creating a pulse of about 18kV.

This circuit seems to rely on the parasitic capacitance of the resistors in order to function. The resistors in this simulator do not have any capacitance, so some 10pF capacitors have been added to get the circuit to work. If you were building this circuit in real life, you would not need those.

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