Plasma breakdown. The voltage across the gas eventually accelerates electrons fast enough that they can ionize atoms when they collide, and an avalanche occurs creating a plasma and light. Same effect as a neon lamp

As the voltage across the gas increases, at some point it causes electrons to leave their valence orbits and travel through the gas (the gas becomes a plasma). That's a "breakdown" if the threshold-crossing causes a sudden, abrupt increase in overall current in the gas, and if the system has a negative resistance trait (one in which the relationship between voltage and current contradicts the usual expectations).

The idea in this case is that the photoelectric effect (Einstein) also can cause an electron to leave its valence orbit. Therefore if the voltage in the gas is high enough to almost cause a breakdown or "avalanche", any extra electrons released by photon interactions may trigger the avalanche in advance of the time it might otherwise have happened.

So you have the possibility of an avalanche caused by the electric field, and you also have some electrons liberated by the photoelectric effect. The breakdown point is determined by both populations, not just one.