Gas is not a very good insulator, so enough voltage will jump an airgap. Once an arc is established between two points, the gas between then is ionised and becomes a lower impedance, meaning that current will continue to flow - and in fact that you need to move those two points further apart than their initial separation to break the arc. Paschen's Law describes the breakdown voltage of a gas, based on gas pressure and voltage across them.
A fluorescent tube relies entirely on this principle. The starter ionises the gas so that the voltage will jump the gap initially, then turns itself off because the spark will stay established. If the starter or tube are faulty so that the gas in the tube is not fully ionised and the spark does not sustain itself, the starter will keep turning on, the spark will keep briefly jumping without properly "taking", and the tube will flash annoyingly.
Fun fact - it's called an "arc" because if you have two points in free air with a horizontal air gap, as this principle was originally demonstrated, the air along the electrical path is heated and tends to rise. The two end points are fixed, but the path of lowest resistance rises with the hot air, so the glowing line of the electrical path starts at the fixed end points and curves up in the middle. The heated air quickly rises out of the electrical path, but of course more comes in behind it. In a sealed tube it naturally doesn't have those convection currents, but the term remains the same.