Joule thief or battery thief. Old technology but they just figured out how to make it small enough to be practical on an existing device.
What these do is just suck most of the remaining energy out of the battery that you would normally throw away.
http://en.wikipedia.org/wiki/Joule_thief
I agree you could get a little more juice out by boosting the voltage. But I have extreme doubts about the 800% claim.