It's basically a pulse-width modulated sawtooth device. Basically, instead of a DC voltage, it shoots pulses, giving you an average voltage of 3.9V or whatever it is tuned for. Basically the pulses help with temperature and power draw. You draw less lower due to the pulsing waveform, since the battery isnt engaged all the time, giving you an average voltage of 0 (it goes from -1 to 1 from what I gather on the site), which means you won't really be able to tell what max voltage it is putting out on a regular multimeter. Also, it lets the heating coil of your atty/carto cool for a split second while the voltage swings downward, probably giving you a bit more longevity with the coils. This may not be true, since the temperature shock of heating and reheating of any type of electrical devices is what causes most damage. However, I suspect that the coil won't really cool down much between pulses, giving it a nice steady temp throughout the use of it. Compared to a DC device, this is I guess their main design principle, since when you press down on a "regular" mod, the coil just gets hotter and hotter until it burns out (if you have no juice and just hold the button down), whereas this mod lets the heater get to a steady-state temperature. I am not affiliated with Akston or anything, I am just an electrical engineer so I am speaking from what I saw on the website and forming general assumptions based on what I currently know.
EDIT: Woops, just saw the video you posted. Nice work on the Oscope! So I guess it uses a square wave with (eyballing) about a 60% duty cycle. It doesnt go from -1 to 1, but 0 to 1 (1 being the max voltage), which makes more sense. I just was looking at the site, and they had a pic of a sawtooth wave. Anyways, pretty interesting device, but I am a bit disappointed that it doesnt have any feedback to control the duty cycle (percentage of time the unit is firing vs off) or voltage, which is kinda lame. I assumed it was a bit smarter. The reason for the not-so-increased battery life is just due to powering the circuitry in addition to providing power to the load. Interesting device, but for the price, I would expect more electrical fanciness since they are going in that direction. Thanks for the review PB!