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This is a "Wenhelt Interrupter". It creates momentary interruptions to the current through the primary coil of a transformer (an automotive ignition coil in this case) to cause a large voltage spike across the primary.

It consists of two electrodes in an electrolyte solution (20% Sodium Hydroxide in this case), but they're separated by a thin-walled non-conductive barrier with a pinhole in it. The pinhole acts like a choke for the current flow, and gets extremely hot very quickly, sort of like the thin wire in a fuse blowing. When it gets hot enough, the water inside the hole boils, and the steam bubble momentarily opens the circuit, causing a huge voltage spike across the primary coil of the transformer, and resulting in the yellow arc you see in the hole.

The voltage spike in the primary is then amplified by the secondary coil, and you get arcs close to ~1" long.

In this example I fed the circuit with mains voltage (120VAC), but alternating current is not a requirement, I simply used it because it was more voltage than most batteries can provide.