I have one of these and opened it up before long out of curiosity as the makers claimed advanced IC circuitry being involved in the iron's workings.
The batteries are directly connected to the two halves of the tip, with the on-off switch cutting the positive. The advanced circuitry is solely involved with the LEDs - Much like Sir Clive Sinclair's LED torch which uses IC control to (apparently) mean that the batteries inside will probably outlast the person using the torch. I have one of these torches and so far so good, it's bright enough for when the mains has just gone and you want to find the candles and despite using it a great deal, it's still going strong - this circuitry seems to do the same thing, stopping the LED light which comes on when soldering from draining the battery too much.
It is in no way connected to the tip, though, I double-checked that. It's simply 3V going straight to the tip halves. From what I understand, as the voltage passes through the two halves (when something shorts them out), the high-resistance material from which the tip is made heats up greatly.
So, it's high resistance turning electrical energy into heat. Like a standard heater element, but using some newfangled material with funky properties.